Image-forming optical system

ABSTRACT

A high-performance image-forming optical system made compact and thin by folding an optical path using reflecting surfaces arranged to minimize the number of reflections. The image-forming optical system has a single prism. When image-side three surfaces of the prism are defined as a surface A, a surface B and a surface C in order from the image plane side thereof, at least one of the surfaces B and C has a rotationally asymmetric curved surface configuration that gives a power to a light beam and corrects aberrations due to decentration. The optical system leads light rays from an object to the image plane without forming an image in the prism and has a pupil in the prism. The surface A is a transmitting surface through which rays exit from the prism. The surfaces B and C are internally reflecting surfaces, which are positioned to face each other to form a Z-shaped optical path.

RELATED APPLICATIONS

This is a divisional of U.S. application Ser. No. 10/852,429, filed May26, 2004, which is a continuation of U.S. application Ser. No.09/417,914 filed Oct. 13, 1999 (now U.S. Pat. No. 6,788,343 issued Sep.7, 2004), and claims priority to Japanese application no. 10-347284,filed Dec. 7, 1998, the entire contents of all of which are incorporatedherein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to image-forming optical systems. Moreparticularly, the present invention relates to a decentered opticalsystem with a reflecting surface having a power for use in opticalapparatus using a small-sized image pickup device, e.g. video cameras,digital still cameras, film scanners, and endoscopes.

Recently, with the achievement of small-sized image pickup devices,image-forming optical systems for use in video cameras, digital stillcameras, film scanners, endoscopes, etc. have also been demanded to bereduced in size and weight and also in cost.

In the general rotationally symmetric coaxial optical systems, however,optical elements are arranged in the direction of the optical axis.Therefore, there is a limit to the reduction in thickness of the opticalsystems. At the same time, the number of lens elements unavoidablyincreases because it is necessary to correct chromatic aberrationproduced by a rotationally symmetric refracting lens used in the opticalsystems. Therefore, it is difficult to reduce the cost in the presentstate of the art. Under these circumstances, there have recently beenproposed optical systems designed to be compact in size by giving apower to a reflecting surface, which produces no chromatic aberration,and folding an optical path in the optical axis direction.

Japanese Patent Application Unexamined Publication (KOKAI) Number[hereinafter referred to as “JP(A)”] 7-333505 proposes to reduce thethickness of an optical system by giving a power to a decenteredreflecting surface and thus folding an optical path. In an examplethereof, however, the number of constituent optical members is as largeas five, and actual optical performance is unclear. No mention is madeof the configuration of the reflecting surface.

JP(A) 8-292371, 9-5650 and 9-90229 each disclose an optical system inwhich an optical path is folded by a single prism or a plurality ofmirrors integrated into a single block, and an image is relayed in theoptical system to form a final image. In these conventional examples,however, the number of reflections increases because the image isrelayed. Accordingly, surface accuracy errors and decentration accuracyerrors are transferred while being added up. Consequently, the accuracyrequired for each surface becomes tight, causing the cost to increaseunfavorably. The relay of the image also causes the overall volumetriccapacity of the optical system to increase unfavorably.

JP(A) 9-222563 discloses an example of an optical system that uses aplurality of prisms. However, because the optical system is arranged torelay an image, the cost increases and the optical system becomes largein size unfavorably for the same reasons as stated above.

JP(A) 9-211331 discloses an example of an optical system in which anoptical path is folded by using a single prism to achieve a reduction insize of the optical system. However, the optical system is notsatisfactorily corrected for aberrations.

JP(A) 8-292368, 8-292372, 9-222561, 9-258105 and 9-258106 all discloseexamples of zoom lens systems. In these examples, however, the number ofreflections is undesirably large because an image is relayed in a prism.Therefore, surface accuracy errors and decentration accuracy errors ofreflecting surfaces are transferred while being added up, unfavorably.At the same time, the overall size of the optical system unavoidablyincreases, unfavorably.

JP (A) 10-20196 discloses an example of a two-unit zoom lens systemhaving a positive front unit and a negative rear unit, in which thepositive front unit comprises a prism of negative power placed on theobject side of a stop and a prism of positive power placed on the imageside of the stop. JP(A) 10-20196 also discloses an example in which thepositive front unit, which comprises a prism of negative power and aprism of positive power, is divided into two to form a three-unit zoomlens system having a negative unit, a positive unit and a negative unit.However, the prisms used in these examples each have two transmittingsurfaces and two reflecting surfaces, which are all independentsurfaces. Therefore, a relatively wide space must be ensured for theprisms. In addition, the image plane is large in size in conformity tothe Leica size film format. Accordingly, the prisms themselves becomeunavoidably large in size. Furthermore, because the disclosed zoom lenssystems are not telecentric on the image side, it is difficult to applythem to image pickup devices such as CCDs. In either of the examples ofzoom lens systems, zooming is performed by moving the prisms.Accordingly, the decentration accuracy required for the reflectingsurfaces becomes tight in order to maintain the required performanceover the entire zooming range, resulting in an increase in the cost.

When a general refracting optical system is used to obtain a desiredrefracting power, chromatic aberration occurs at an interface surfacethereof according to chromatic dispersion characteristics of an opticalelement. To correct the chromatic aberration and also correct other rayaberrations, the refracting optical system needs a large number ofconstituent elements, causing the cost to increase. In addition, becausethe optical path extends straight along the optical axis, the entireoptical system undesirably lengthens in the direction of the opticalaxis, resulting in an unfavorably large-sized image pickup apparatus.

In decentered optical systems such as those described above in regard tothe prior art, an imaged figure or the like is undesirably distorted andthe correct shape cannot be reproduced unless the formed image isfavorably corrected for aberrations, particularly rotationallyasymmetric distortion.

Furthermore, in a case where a reflecting surface is used in adecentered optical system, the sensitivity to decentration errors of thereflecting surface is twice as high as that in the case of a refractingsurface, and as the number of reflections increases, decentration errorsthat are transferred while being added up increase correspondingly.Consequently, manufacturing accuracy and assembly accuracy, e.g. surfaceaccuracy and decentration accuracy, required for reflecting surfacesbecome even more strict.

SUMMARY OF THE INVENTION

In view of the above-described problems of the prior art, an object ofthe present invention is to provide a high-performance and low-costimage-forming optical system having a reduced number of constituentoptical elements.

Another object of the present invention is to provide a high-performanceimage-forming optical system that is made compact and thin by folding anoptical path using reflecting surfaces arranged to minimize the numberof reflections.

To attain the above-described objects, the present invention provides animage-forming optical system having a positive refracting power as awhole for forming an object image. The image-forming optical system hasat least one prism formed from a medium having a refractive index (n)larger than 1.3 (n>1.3). The prism has at least four optical surfacesthat transmit or reflect a light beam. When image-side three surfaces ofthe at least four optical surfaces are defined as a surface A, a surfaceB and a surface C in order from the image plane side of the prism, atleast one of the surfaces B and C has a curved surface configurationthat gives a power to a light beam. The curved surface configuration hasa rotationally asymmetric surface configuration that correctsaberrations due to decentration. The image-forming optical system leadslight rays from an object to the image plane without forming an image inthe prism and has a pupil in the prism. The surface A has a transmittingaction by which rays internally reflected from the surface B are allowedto exit from the prism. The surface B has a reflecting action to reflectrays internally reflected from the surface C. The surface C has areflecting action.

The reasons for adopting the above-described arrangement in the presentinvention, together with the function thereof, will be described belowin order.

The image-forming optical system according to the present invention,which is provided to attain the above-described objects, has a positiverefracting power as a whole for forming an object image. Theimage-forming optical system has at least one prism formed from a mediumhaving a refractive index (n) larger than 1.3 (n>1.3). The prism has atleast four optical surfaces that transmit or reflect a light beam. Theimage-forming optical system leads light rays from an object to theimage plane without forming an image in the prism and has a pupil in theprism.

A refracting optical element such as a lens is provided with a power bygiving a curvature to an interface surface thereof. Accordingly, whenrays are refracted at the interface surface of the lens, chromaticaberration unavoidably occurs according to chromatic dispersioncharacteristics of the refracting optical element. Consequently, thecommon practice is to add another refracting optical element for thepurpose of correcting the chromatic aberration.

Meanwhile, a reflecting optical element such as a mirror or a prismproduces no chromatic aberration in theory even when a reflectingsurface thereof is provided with a power, and need not add anotheroptical element only for the purpose of correcting chromatic aberration.Accordingly, an optical system using a reflecting optical element allowsthe number of constituent optical elements to be reduced from theviewpoint of chromatic aberration correction in comparison to an opticalsystem using a refracting optical element.

At the same time, a reflecting optical system using a reflecting opticalelement allows the optical system itself to be compact in size incomparison to a refracting optical system because the optical path isfolded in the reflecting optical system.

Reflecting surfaces require a high degree of accuracy for assembly andadjustment because they have high sensitivity to decentration errors incomparison to refracting surfaces. However, among reflecting opticalelements, prisms, in which the positional relationship between surfacesis fixed, only need to control decentration as a single unit of prismand do not need high assembly accuracy and a large number of man-hoursfor adjustment as are needed for other reflecting optical elements.

Furthermore, a prism has an entrance surface and an exit surface, whichare refracting surfaces, and a reflecting surface. Therefore, the degreeof freedom for aberration correction is high in comparison to a mirror,which has only a reflecting surface. In particular, if the prismreflecting surface is assigned the greater part of the desired power tothereby reduce the powers of the entrance and exit surfaces, which arerefracting surfaces, it is possible to reduce chromatic aberration to avery small quantity in comparison to refracting optical elements such aslenses while maintaining the degree of freedom for aberration correctionat a high level in comparison to mirrors. Furthermore, the inside of aprism is filled with a transparent medium having a refractive indexhigher than that of air. Therefore, it is possible to obtain a longeroptical path length than in the case of air. Accordingly, the use of aprism makes it possible to obtain an optical system that is thinner andmore compact than those formed from lenses, mirrors and so forth, whichare placed in the air.

In addition, an image-forming optical system is required to exhibitfavorable image-forming performance as far as the peripheral portions ofthe image field, not to mention the performance required for the centerof the image field. In the case of a general coaxial optical system, thesign of the ray height of extra-axial rays is inverted at a stop.Accordingly, if optical elements are not in symmetry with respect to thestop, off-axis aberrations are aggravated. For this reason, the commonpractice is to place refracting surfaces at respective positions facingeach other across the stop, thereby obtaining a satisfactory symmetrywith respect to the stop, and thus correcting off-axis aberrations.

For the reasons stated above, the present invention adopts a basicarrangement in which the image-forming optical system has a stop in theprism and does not form an intermediate image. In addition, it isdesirable that the image-forming optical system should be approximatelytelecentric on the image side.

Next, the arrangement of an image-forming optical system that isapproximately telecentric on the image side will be described in detail.

As has been stated above, reflecting surfaces have a high decentrationerror sensitivity in comparison to refracting surfaces. Therefore, it isdesirable to provide an arrangement of an optical system that is asindependent of the high decentration error sensitivity as possible. Inthe case of a general coaxial optical system arranged to beapproximately telecentric on the image side, because extra-axialprincipal rays are approximately parallel to the optical axis, thepositional accuracy of the extra-axial rays is satisfactorily maintainedon the image plane even if defocusing is effected. Therefore, theimage-forming optical system according to the present invention isarranged to reflect the property of the above-described arrangement. Inparticular, to prevent the performance of an optical system using areflecting surface, which has a relatively high decentration errorsensitivity, from being deteriorated by focusing, it is desirable toadopt an arrangement in which the optical system is approximatelytelecentric on the image side, whereby the positional accuracy ofextra-axial rays is maintained favorably.

Such an arrangement enables the present invention to be suitably appliedto an image pickup optical system using an image pickup device, e.g. aCCD, in particular. Adopting the above-described arrangement minimizesthe influence of the cosine fourth law. Accordingly, it is also possibleto reduce shading.

As has been stated above, adopting the basic arrangement of the presentinvention makes it possible to obtain a compact image-forming opticalsystem that has a smaller number of constituent optical elements than inthe case of a refracting optical system and exhibits favorableperformance throughout the image field, from the center to the peripherythereof.

Incidentally, the prism in the present invention has an image-side partincluding reflecting and transmitting surfaces. That is, the image-sidepart of the prism includes a surface C that reflects in the prism alight beam passing through a first transmitting surface placed in afront-half part of the prism to allow a light beam to enter the prism(in a case where another reflecting surface is provided, the surface Creflects the light beam reflected from the reflecting surface). Thesurfaces in the image-side part of the prism further include a surface Bthat reflects in the prism the light beam reflected from the surface C,and a surface A through which the light beam exits from the prism. Atleast one of the surfaces B and C has a curved surface configurationthat gives a power to a light beam. The curved surface configuration hasa rotationally asymmetric surface configuration that correctsaberrations due to decentration.

An object-side part of the prism in the present invention, exclusive ofthe surfaces A, B and C, has at least one reflecting surface thatreflects a light beam in the prism (the object-side part willhereinafter be referred to as the “prism object-side part”, and the partincluding the surfaces A, B and C as the “prism image-side part”). Thereflecting surface has a rotationally asymmetric surface configurationthat gives a power to a light beam and corrects aberrations due todecentration.

When a light ray from the object center that passes through the centerof the stop and reaches the center of the image plane is defined as anaxial principal ray, it is desirable that the at least one reflectingsurface in the prism object-side part should be decentered with respectto the axial principal ray. If the at least one reflecting surface inthe prism object-side part is not decentered with respect to the axialprincipal ray, the axial principal ray travels along the same opticalpath when incident on and reflected from the reflecting surface, andthus the axial principal ray is intercepted in the optical systemundesirably. As a result, an image is formed from only a light beamwhose central portion is shaded. Consequently, the center of the imageis unfavorably dark, or no image is formed in the center of the imagefield.

It is also possible to decenter a reflecting surface with a power withrespect to the axial principal ray.

When a reflecting surface with a power is decentered with respect to theaxial principal ray, it is desirable that at least one of surfacesconstituting the prism used in the present invention should be arotationally asymmetric surface. In the prism image-side part, it isparticularly preferable from the viewpoint of aberration correction thatat least one of the surfaces C and B, which are reflecting surfaces,should be a rotationally asymmetric surface. In the prism object-sidepart, it is particularly preferable from the viewpoint of aberrationcorrection that the at least one reflecting surface should be arotationally asymmetric surface.

The reasons for adopting the above-described arrangements in the presentinvention will be described below in detail.

First, a coordinate system used in the following description androtationally asymmetric surfaces will be described.

An optical axis defined by a straight line along which the axialprincipal ray travels until it intersects the first surface of theoptical system is defined as a Z-axis. An axis perpendicularlyintersecting the Z-axis in the decentration plane of each surfaceconstituting the image-forming optical system is defined as a Y-axis. Anaxis perpendicularly intersecting the optical axis and alsoperpendicularly intersecting the Y-axis is defined as an X-axis. Raytracing is forward ray tracing in which rays are traced from the objecttoward the image plane.

In general, a spherical lens system comprising only a spherical lens isarranged such that aberrations produced by spherical surfaces, such asspherical aberration, coma and curvature of field, are corrected withsome surfaces by canceling the aberrations with each other, therebyreducing aberrations as a whole.

On the other hand, rotationally symmetric aspherical surfaces and thelike are used to correct aberrations favorably with a minimal number ofsurfaces. The reason for this is to reduce various aberrations thatwould be produced by spherical surfaces.

However, in a decentered optical system, rotationally asymmetricaberrations due to decentration cannot be corrected by a rotationallysymmetric optical system. Rotationally asymmetric aberrations due todecentration include distortion, curvature of field, and astigmatic andcomatic aberrations, which occur even on the axis.

First, rotationally asymmetric curvature of field will be described. Forexample, when rays from an infinitely distant object point are incidenton a decentered concave mirror, the rays are reflected by the concavemirror to form an image. In this case, the back focal length from thatportion of the concave mirror on which the rays strike to the imagesurface is a half the radius of curvature of the portion on which therays strike in a case where the medium on the image side is air.Consequently, as shown in FIG. 18, an image surface tilted with respectto the axial principal ray is formed. It is impossible to correct suchrotationally asymmetric curvature of field by a rotationally symmetricoptical system.

To correct the tilted curvature of field by the concave mirror M itself,which is the source of the curvature of field, the concave mirror M isformed from a rotationally asymmetric surface, and, in this example, theconcave mirror M is arranged such that the curvature is made strong(refracting power is increased) in the positive direction of the Y-axis,whereas the curvature is made weak (refracting power is reduced) in thenegative direction of the Y-axis. By doing so, the tilted curvature offield can be corrected. It is also possible to obtain a flat imagesurface with a minimal number of constituent surfaces by placing arotationally asymmetric surface having the same effect as that of theabove-described arrangement in the optical system separately from theconcave mirror M.

It is preferable that the rotationally asymmetric surface should be arotationally asymmetric surface having no axis of rotational symmetry inthe surface nor out of the surface. If the rotationally asymmetricsurface has no axis of rotational symmetry in the surface nor out of thesurface, the degree of freedom increases, and this is favorable foraberration correction.

Next, rotationally asymmetric astigmatism will be described.

A decentered concave mirror M produces astigmatism even for axial rays,as shown in FIG. 19, as in the case of the above. The astigmatism can becorrected by appropriately changing the curvatures in the X- and Y-axisdirections of the rotationally asymmetric surface as in the case of theabove.

Rotationally asymmetric coma will be described below.

A decentered concave mirror M produces coma even for axial rays, asshown in FIG. 20, as in the case of the above. The coma can be correctedby changing the tilt of the rotationally asymmetric surface according asthe distance from the origin of the X-axis increases, and furtherappropriately changing the tilt of the surface according to the sign(positive or negative) of the Y-axis.

The image-forming optical system according to the present invention mayalso be arranged such that the above-described at least one surfacehaving a reflecting action is decentered with respect to the axialprincipal ray and has a rotationally asymmetric surface configurationand further has a power. By adopting such an arrangement, decentrationaberrations produced as the result of giving a power to the reflectingsurface can be corrected by the surface itself. In addition, the powerof the refracting surfaces of the prism is reduced, and thus chromaticaberration produced in the prism can be minimized.

The rotationally asymmetric surface used in the present invention shouldpreferably be a plane-symmetry free-form surface having only one planeof symmetry. Free-form surfaces used in the present invention aredefined by the following equation (a). It should be noted that theZ-axis of the defining equation is the axis of a free-form surface.

$\begin{matrix}{Z = {{{cr}^{2}/\left\lbrack {1 + \left. \sqrt{}\left\{ {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\} \right.} \right\rbrack} + {\sum\limits_{j = 2}^{66}{C_{j}X^{m}Y^{n}}}}} & (a)\end{matrix}$

In Eq. (a), the first term is a spherical surface term, and the secondterm is a free-form surface term.

In the spherical surface term:

-   -   c: the curvature at the vertex    -   k: a conic constant    -   r=√(X²+Y²)

The free-form surface term is given by

${\sum\limits_{j = 2}^{66}{C_{j}X^{m}Y^{n}}} = {{C_{2}X} + {C_{3}Y} + {C_{4}X^{2}} + {C_{5}{XY}} + {C_{6}Y^{2}} + {C_{7}X^{3}} + {C_{8}X^{2}Y} + {C_{9}{XY}^{2}} + {C_{10}Y^{3}} + {C_{11}X^{4}} + {C_{12}X^{3}Y} + {C_{13}X^{2}Y^{2}} + {C_{14}{XY}^{3}} + {C_{15}Y^{4}} + {C_{16}X^{5}} + {C_{17}X^{4}Y} + {C_{18}X^{3}Y^{2}} + {C_{19}X^{2}Y^{3}} + {C_{20}{XY}^{4}} + {C_{21}Y^{5}} + {C_{22}X^{6}} + {C_{23}X^{5}Y} + {C_{24}X^{4}Y^{2}} + {C_{25}X^{3}Y^{3}} + {C_{26}X^{2}Y^{4}} + {C_{27}{XY}^{5}} + {C_{28}Y^{6}} + {C_{29}X^{7}} + {C_{30}X^{6}Y} + {C_{31}X^{5}Y^{2}} + {C_{32}X^{4}Y^{3}} + {C_{33}X^{3}Y^{4}} + {C_{34}X^{2}Y^{5}} + {C_{35}{XY}^{6}} + {C_{36}Y^{7}}}$

where C_(j) (j is an integer of 2 or higher) are coefficients.

In general, the above-described free-form surface does not have planesof symmetry in both the XZ- and YZ-planes. In the present invention,however, a free-form surface having only one plane of symmetry parallelto the YZ-plane is obtained by making all terms of odd-numbered degreeswith respect to X zero. For example, in the above defining equation (a),the coefficients of the terms C₂, C₅, C₇, C₉, C₁₂, C₁₄, C₁₆, C₁₈, C₂₀,C₂₃, C₂₅, C₂₇, C₂₉, C₃₁, C₃₃, C₃₅, . . . are set equal to zero. By doingso, it is possible to obtain a freeform surface having only one plane ofsymmetry parallel to the YZ-plane.

A free-form surface having only one plane of symmetry parallel to theXZ-plane is obtained by making all terms of odd-numbered degrees withrespect to Y zero. For example, in the above defining equation (a), thecoefficients of the terms C₃, C₅, C₈, C₁₀, C₁₂, C₁₄, C₁₇, C₁₉, C₂₁, C₂₃,C₂₅, C₂₇, C₃₀, C₃₂, C₃₄, C₃₆, . . . are set equal to zero. By doing so,it is possible to obtain a free-form surface having only one plane ofsymmetry parallel to the XZ-plane.

Furthermore, the direction of decentration is determined incorrespondence to either of the directions of the above-described planesof symmetry. For example, with respect to the plane of symmetry parallelto the YZ-plane, the direction of decentration of the optical system isdetermined to be the Y-axis direction. With respect to the plane ofsymmetry parallel to the XZ-plane, the direction of decentration of theoptical system is determined to be the X-axis direction. By doing so,rotationally asymmetric aberrations due to decentration can be correctedeffectively, and at the same time, productivity can be improved.

It should be noted that the above defining equation (a) is shown asmerely an example, and that the feature of the present invention residesin that rotationally asymmetric aberrations due to decentration arecorrected and, at the same time, productivity is improved by using arotationally asymmetric surface having only one plane of symmetry.Therefore, the same advantageous effect can be obtained for any otherdefining equation that expresses such a rotationally asymmetric surface.

In the present invention, the prism object-side part and the prismimage-side part may be made of different materials and cementedtogether. Alternatively, the prism object-side part and the prismimage-side part may be placed adjacently to each other with a smallspacing therebetween. In either case, the advantageous effects of thepresent invention can be obtained satisfactorily.

Incidentally, it is desirable to arrange the prism optical system suchthat the two reflecting surfaces C and B, which are placed in theimage-side part of the prism optical system, are positioned to face eachother across the prism medium, and the surface A, which has atransmitting action by which a light beam is allowed to exit from theprism, is disposed between the surfaces C and B, thereby forming aZ-shaped optical path.

As stated above, the surfaces A to C in the prism image-side part arearranged to form a Z-shaped optical path in the prism. In other words,the surfaces A to C are arranged such that optical paths in the prism donot intersect each other. With the above-described arrangement,directions in which the axial principal ray is incident on and reflectedfrom the surface C, respectively, are opposite to directions in whichthe axial principal ray are incident on and reflected from the surfaceB. Accordingly, it is easy to correct the optical system foraberrations, and the arrangement is favorable from the viewpoint ofdesign and aberration correcting performance.

By arranging the prism image-side part as stated above, the angle ofreflection in the prism image-side part can be made gentle in comparisonto a prism structure in which the entrance position to the prismimage-side part and the exit surface are adjacent to each other.Accordingly, the aggravation of aberrations is reduced, and the degreeof design freedom increases.

If the prism image-side part is constructed by using two reflectingsurfaces and one transmitting surface as stated above, the degree offreedom for aberration correction increases, and the amount ofaberration produced in the prism image-side part is favorably small. Inaddition, because the relative decentration between the two reflectingsurfaces is small, aberrations produced by the two reflecting surfacesare corrected with these reflecting surfaces by canceling theaberrations each other. Therefore, the amount of aberration produced inthe prism is favorably small. It is more desirable that the tworeflecting surfaces should have powers of different signs. By doing so,it is possible to enhance the effect of correcting each other'saberrations by the two reflecting surfaces and hence possible to obtainhigh resolution.

It is preferable to minimize the relative decentration between thesurfaces C and B at the respective positions where the optical axis isreflected. By doing so, it is possible to minimize the amount ofdecentration aberrations. Thus, the amount of rotationally asymmetricaberrations produced in the prism becomes small.

Accordingly, both the surfaces C and B of the prism image-side part maybe arranged to have a rotationally asymmetric surface configuration thatgives a power to a light beam and corrects aberrations due todecentration.

Furthermore, the rotationally asymmetric surface configuration of atleast one of the surfaces C and B in the prism image-side part may bearranged in the form of a plane-symmetry free-form surface having onlyone plane of symmetry.

When both the surfaces C and B of the prism image-side part haverotationally asymmetric surface configurations, the rotationallyasymmetric surface configuration of each of the two surfaces may bearranged in the form of a plane-symmetry free-form surface having onlyone plane of symmetry.

In this case, the prism image-side part may be arranged such that theonly one plane of symmetry of the plane-symmetry free-form surface thatforms the surface C and the only one plane of symmetry of theplane-symmetry free-form surface that forms the surface B are formed inthe same plane.

The surface A of the prism image-side part may have a rotationallyasymmetric surface configuration that gives a power to a light beam andcorrects aberrations due to decentration. A refracting surface havingsuch a surface configuration is effective in correcting aberrations dueto decentration.

In this case, the rotationally asymmetric surface configuration of thesurface A of the prism image-side part may be arranged in the form of aplane-symmetry free-form surface having only one plane of symmetry.

Furthermore, a rotationally asymmetric surface placed in the prismobject-side part may be arranged in the form of a plane-symmetryfree-form surface having only one plane of symmetry.

The arrangement may be such that the prism object-side part and theprism image-side part each have at least one plane-symmetry free-formsurface having only one plane of symmetry, and the only one plane ofsymmetry of the at least one plane-symmetry free-form surface in theprism object-side part and that of the at least one plane-symmetryfree-form surface in the prism image-side part are placed in the sameplane.

By using a reflecting surface having a negative refracting power to formthe prism object-side part, a wide field angle for imaging can beobtained. This is because the negative power enables rays of wide fieldangle to be converged and thus it is possible to converge the light beamwhen the rays are incident on a reflecting surface provided in the prismimage-side part. This is favorable from the viewpoint of aberrationcorrection when an optical system having a relatively short focal lengthis to be constructed.

In the present invention, the effective way of enhancing the symmetryrequired for the image-forming optical system and thereby favorablycorrecting aberrations, including off-axis aberrations, is to place apupil between the prism object-side part and the prism image-side partand to place the prism image-side part between the pupil and the imageplane.

In this case, a stop can be placed on the pupil (particularly, in a casewhere the prism object-side part and the prism image-side part arecemented together, or they are placed adjacently to each other with asmall spacing therebetween).

In the present invention, the prism object-side part, exclusive of thesurfaces A, B and C, may be arranged to have two or more reflectingsurfaces with a curved surface configuration that gives a power to alight beam.

In this case, the prism object-side part, exclusive of the surfaces A, Band C, may be formed from two optical surfaces, i.e. an entrance surfaceserving as both a reflecting surface and a transmitting surface, and areflecting surface. In other words, the second reflecting surface andthe first transmitting surface may be formed from a single surfaceserving as both reflecting and transmitting surfaces. With thisarrangement, the first reflecting surface reflects incident rays towardthe second reflecting surface at a minimal angle of deviation, and thesecond reflecting surface bends the rays to a considerable extent.Therefore, it is possible to reduce the thickness of the prism in thedirection of the incident rays.

In a case where the prism object-side part is arranged as stated above,it is preferable to give a negative power to the first reflectingsurface (a positive power may be locally present in the first reflectingsurface). By doing so, it is possible to lengthen the optical pathlength along an optical path between the first reflecting surface and asurface having a positive power in the prism image-side part.Consequently, the positive and negative powers of the two surfaces canbe weakened, and it becomes possible to minimize aberrations produced bythese surfaces. Thus, it is possible to maintain the required aberrationcorrecting performance and to widen the field angle most effectively.

It is preferable to place the stop on the image side of the prismobject-side part. By doing so, in a case where the first reflectingsurface has a negative power and is approximated by a spherical surface,the center of curvature of the first reflecting surface and the stopposition are approximately coincident with each other. Therefore, it ispossible to eliminate comatic aberration in theory.

In the present invention, the prism object-side part, exclusive of thesurfaces A, B and C, may comprise an entrance surface having atransmitting action by which a light beam is allowed to enter the prism,and two reflecting surfaces that give a power to a light beam.

In this case, it is particularly desirable to arrange the prismobject-side part such that the two reflecting surfaces face each otheracross the prism medium, and the entrance surface and the two reflectingsurfaces form a Z-shaped optical path.

The above-described prism configuration enables an increase in thedegree of freedom for aberration correction and produces minimalaberrations. In addition, because the relative decentration between thetwo reflecting surfaces is small, aberrations produced by the tworeflecting surfaces are corrected with these reflecting surfaces bycanceling the aberrations each other. Therefore, the amount ofaberration produced in the prism is favorably small. It is moredesirable that the two reflecting surfaces should have powers ofdifferent signs. By doing so, it is possible to enhance the effect ofcorrecting each other's aberrations by the two reflecting surfaces andhence possible to obtain high resolution.

It is even more desirable to give a negative power to the firstreflecting surface. By doing so, it is possible to lengthen the opticalpath length along an optical path between the first reflecting surfaceand a surface having a positive power in the prism image-side part.Consequently, the positive and negative powers of the two surfaces canbe weakened, and it becomes possible to minimize aberrations produced bythese surfaces. It is also preferable to place the stop on the imageside of the prism object-side part. By doing so, in a case where thefirst reflecting surface has a negative power and is approximated by aspherical surface, the center of curvature of the first reflectingsurface and the stop position are approximately coincident with eachother. Therefore, it is possible to eliminate comatic aberration intheory.

In the present invention, the prism object-side part, exclusive of thesurfaces A, B and C, may be formed from three optical surfaces, i.e. anentrance surface serving as both a reflecting surface and a transmittingsurface, and two reflecting surfaces.

In this type of prism, the first transmitting surface and the secondreflecting surface are formed from a single surface serving as bothtransmitting and reflecting surfaces. The first reflecting surfacereflects incident rays toward the second reflecting surface at a minimalangle of deviation. The second reflecting surface bends rays to aconsiderable extent. The third reflecting surface bends rays at aminimal angle of deviation. Therefore, it is possible to reduce thethickness of the prism in the direction of the incident rays. Inaddition, in a case where a stop is placed between the prism object-sidepart and the prism image-side part, it is possible to lengthen theoptical path length from the stop position to the first reflectingsurface, which usually has a strong negative refracting power, in theprism. Accordingly, a thin optical system can be constructed. Moreover,the distance between the prism object-side part and the prism image-sidepart can be shortened.

By arranging the prism object-side part to have a negative refractingpower, a wide field angle for imaging can be obtained. This is becausethe negative power enables rays of wide field angle to be converged andthus it is possible to converge the light beam when the rays areincident on the second unit, which comprises the prism image-side part.This is favorable from the viewpoint of aberration correction when anoptical system having a relatively short focal length is to beconstructed.

When a prism object-side part having the above-described arrangement isused, it is preferable for the second reflecting surface to effect thereflection in the prism by a totally reflecting action so as to serve asboth transmitting and reflecting surfaces.

In addition, it is preferable for the first reflecting surface of theprism object-side part to have a reflecting surface configuration thatgives a negative power to a light beam reflected in the prism as a whole(a positive power may be locally present in the first reflectingsurface).

By virtue of the above-described arrangement, it is possible to lengthenthe optical path length along an optical path between the firstreflecting surface and a surface having a positive power in the prismimage-side part. Consequently, the positive and negative powers of thetwo surfaces can be weakened, and it becomes possible to minimizeaberrations produced by these surfaces. Thus, it is possible to maintainthe required aberration correcting performance and to widen the fieldangle most effectively.

In the prism of the present invention, reflecting surfaces other than atotally reflecting surface are preferably formed from a reflectingsurface having a thin film of a metal, e.g. aluminum or silver, formedon the surface thereof, or a reflecting surface formed from a dielectricmultilayer film. In the case of a metal thin film having reflectingaction, a high reflectivity can be readily obtained. The use of adielectric reflecting film is advantageous in a case where a reflectingfilm having wavelength selectivity or minimal absorption is to beformed.

Thus, it is possible to obtain a low-cost and compact image-formingoptical system in which the prism manufacturing accuracy is favorablyeased.

In the present invention, it is desirable for the image-forming opticalsystem to have a prism object-side part having a diverging action on theobject side of a stop and a prism image-side part having a convergingaction on the image side of the stop, and also desirable for theimage-forming optical system to be approximately telecentric on theimage side.

In an image-forming optical system using a refracting optical element,the power distribution varies according to the use application. Forexample, telephoto systems having a narrow field angle generally adoptan arrangement in which the entire system is formed as a telephoto typehaving a positive front unit and a negative rear unit, thereby makingthe overall length of the optical system shorter than the focal length.Wide-angle systems having a wide field angle generally adopt anarrangement in which the entire system is formed as a retrofocus typehaving a negative front unit and a positive rear unit, thereby makingthe back focus longer than the focal length.

In the case of an image-forming optical system using an image pickupdevice, e.g. a CCD, in particular, it is necessary to place an opticallow-pass filter, an infrared cutoff filter, etc. between theimage-forming optical system and the image pickup device to remove moireand to eliminate the influence of infrared rays. Therefore, with a viewto ensuring a space for placing these optical members, it is desirableto adopt a retrofocus type arrangement for the image-forming opticalsystem.

It is important for a retrofocus type image-forming optical system to becorrected for aberrations, particularly off-axis aberrations. Thecorrection of off-axis aberrations depends largely on the position ofthe stop. As has been stated above, in the case of a general coaxialoptical system, off-axis aberrations are aggravated if optical elementsare not in symmetry with respect to the stop. For this reason, thecommon practice is to place optical elements of the same sign atrespective positions facing each other across the stop, therebyobtaining a satisfactory symmetry with respect to the stop, and thuscorrecting off-axis aberrations. In the case of a retrofocus type systemhaving a negative front unit and a positive rear unit, the powerdistribution is asymmetric in the first place. Therefore, the off-axisaberration-correcting performance varies to a considerable extentaccording to the position of the stop.

Therefore, the stop is placed between the prism object-side part havinga diverging action and the prism image-side part having a convergingaction, thereby making it possible to minimize the aggravation ofoff-axis aberrations due to the asymmetry of the power distribution. Ifthe stop is placed on the object side of the prism object-side parthaving a diverging action or on the image side of the prism image-sidepart having a converging action, the asymmetry with respect to the stopis enhanced and becomes difficult to correct.

In this case, the image-forming optical system may consist of a prism inwhich the prism object-side part of diverging action is placed on theobject side of the stop, and the prism image-side part of convergingaction is placed on the image side of the stop.

In the image-forming optical systems according to the present invention,there is only one image-formation plane throughout the system. As hasbeen stated above, the decentration error sensitivity of a reflectingsurface is higher than that of a refracting surface. In a reflectingoptical member arranged in the form of a single block as in the case ofa prism, surface accuracy errors and decentration errors of each surfaceare transferred while being added up. Therefore, the smaller the numberof reflecting surfaces, the more the manufacturing accuracy required foreach surface is eased. Accordingly, it is undesirable to increase thenumber of reflections more than is needed. For example, in animage-forming optical system in which an intermediate image is formedand this image is relayed, the number of reflections increases more thanis needed, and the manufacturing accuracy required for each surfacebecomes tight, causing the cost to increase unfavorably.

Let us define the power of a decentered optical system and that of adecentered optical surface. As shown in FIG. 21, when the direction ofdecentration of a decentered optical system S is taken in the Y-axisdirection, a light ray which is parallel to the axial principal ray ofthe decentered optical system S and which has a small height d in theYZ-plane is made to enter the decentered optical system S from theobject side thereof. The angle that is formed between that ray and theaxial principal ray exiting from the decentered optical system S as thetwo rays are projected onto the YZ-plane is denoted by δy, and δy/d isdefined as the power Py in the Y-axis direction of the decenteredoptical system S. Similarly, a light ray which is parallel to the axialprincipal ray of the decentered optical system S and which has a smallheight d in the X-axis direction, which is perpendicular to theYZ-plane, is made to enter the decentered optical system S from theobject side thereof. The angle that is formed between that ray and theaxial principal ray exiting from the decentered optical system S as thetwo rays are projected onto a plane perpendicularly intersecting theYZ-plane and containing the axial principal ray is denoted by δx, andδx/d is defined as the power Px in the X-axis direction of thedecentered optical system S. The power Pyn in the Y-axis direction andpower Pxn in the X-axis direction of a decentered optical surface nconstituting the decentered optical system S are defined in the same wayas the above.

Furthermore, the reciprocals of the above-described powers are definedas the focal length Fy in the Y-axis direction of the decentered opticalsystem S, the focal length Fx in the X-axis direction of the decenteredoptical system S, the focal length Fyn in the Y-axis direction of thedecentered optical surface n, and the focal length Fxn in the X-axisdirection of the decentered optical surface n, respectively.

When the powers in the X- and Y-axis directions of the surface B havinga reflecting action are denoted by Pxb and Pyb, respectively, and thepowers in the X- and Y-axis directions of the prism are denoted by Pxand Py, respectively, it is preferable to satisfy the followingcondition:

0<Pxb/Px<5  (1)

The condition (1) limits the power of the surface B having a reflectingaction in the prism image-side part. The surface B needs to have arelatively strong power in the whole optical system. The surface B ischaracterized in that because it has a relatively small amount ofdecentration with respect to rays, even if the surface B has a strongpower, it produces a relatively small amount of decentrationaberrations.

If Pxb/Px is not larger than the lower limit of the condition (1), i.e.0, the surface B has no power. Consequently, another surface needs tohave a strong power, and the amount of decentration aberrations producedby this surface becomes unfavorably large. If Pxb/Px is not smaller thanthe upper limit of the condition (1), i.e. 5, the power of the surface Bbecomes excessively strong, and the amount of decentration aberrationsproduced by the surface B becomes unfavorably large.

It is even more desirable to satisfy the following condition:

0<Pxb/Px<2  (1-1)

It is still more desirable to satisfy the following condition:

0<Pxb/Px<1  (1-2)

It is also preferable to satisfy the following condition:

0<Pyb/Py<5  (2)

The meaning of the condition (2) is the same as that of the condition(1). Therefore, a description thereof is omitted.

It is even more desirable to satisfy the following condition:

0<Pyb/Py<2  (2-1)

It is still more desirable to satisfy the following condition:

0<Pyb/Py<1  (2-2)

When the powers in the X- and Y-axis directions of the surface C havinga reflecting action are denoted by Pxc and Pyc, respectively, and thepowers in the X- and Y-axis directions of the prism are denoted by Pxand Py, respectively, it is preferable to satisfy the followingcondition:

−5<Pxc/Px<5  (3)

The condition (3) limits the power of the surface C having a reflectingaction in the prism image-side part. The surface C needs to have arelatively strong power in the whole optical system. The surface C ischaracterized in that because it has a relatively small amount ofdecentration with respect to rays, even if the surface C has a strongpower, it produces a relatively small amount of decentrationaberrations.

If Pxc/Px is not larger than the lower limit of the condition (3), i.e.−5, the negative power of the surface C becomes excessively strong.Consequently, another surface needs to have a strong positive power, andthe amount of decentration aberrations produced by this surface becomesunfavorably large. If Pxc/Px is not smaller than the upper limit of thecondition (3), i.e. 5, the power of the surface C becomes excessivelystrong, and the amount of decentration aberrations produced by thesurface C becomes unfavorably large.

It is even more desirable to satisfy the following condition:

−2<Pxc/Px<2  (3-1)

It is still more desirable to satisfy the following condition:

−1<Pxc/Px<1  (3-2)

It is also preferable to satisfy the following condition:

−5<Pyc/Py<5  (4)

The meaning of the condition (4) is the same as that of the condition(3). Therefore, a description thereof is omitted.

It is even more desirable to satisfy the following condition:

−2<Pyc/Py<2  (4-1)

It is still more desirable to satisfy the following condition:

−1<Pyc/Py<1  (4-2)

Next, when the incident angles of the axial principal ray on thesurfaces B and C are denoted by αb and αc, respectively, it ispreferable to satisfy the following condition:

5°<αb<45°  (5)

The condition (5) relates to the power of the surface B. If αb is notlarger than the lower limit of the condition (5), i.e. 5°, rays incidenton the surface B are undesirably intercepted by the surface C.Accordingly, it becomes impossible to construct the desired opticalsystem. If αb is not smaller than the upper limit of the condition (5),i.e. 45°, the amount of decentration becomes excessively large.Consequently, decentration aberrations produced by the surface B becomeexcessively large and hence impossible to correct by another surface.

It is even more desirable to satisfy the following condition:

10°<αb<40°  (5-1)

It is still more desirable to satisfy the following conditions:

20°<αb<30°  (5-2)

It is also preferable to satisfy the following condition:

5°<αc<45°  (6)

The condition (6) relates to the power of the surface C. If αc is notlarger than the lower limit of the condition (6), i.e. 5°, rays incidenton the surface C are undesirably intercepted by the surface B.Accordingly, it becomes impossible to construct the desired opticalsystem. If αc is not smaller than the upper limit of the condition (6),i.e. 45°, the amount of decentration becomes excessively large.Consequently, decentration aberrations produced by the surface C becomeexcessively large and hence impossible to correct by another surface.

It is even more desirable to satisfy the following condition:

10°<αc<40°  (6-1)

It is still more desirable to satisfy the following conditions:

20°<αc<30°  (6-2)

Next, when the ratio of αc to αb, i.e. αc/αb, is denoted by αbc, it ispreferable to satisfy the following condition:

0.6<αbc<1.4  (7)

The condition (7) is a condition for a portion of the prism image-sidepart that forms a Z-shaped optical path. The feature of the Z-shapedoptical path resides in that the optical path length from a point on thesurface C at which the axial principal ray is reflected by the surface Cto a point on the surface B at which the axial principal ray isreflected by the surface B is relatively uniform independently of thefield angle. Thus, the resultant total power of the two reflectingsurfaces C and B is uniform independently of the field angle,advantageously.

If αbc is not larger than the lower limit of the condition (7), i.e.0.6, or not smaller than the upper limit, i.e. 1.4, the Z-shaped opticalpath is unfavorably distorted, and decentration aberrations produced bythe surfaces B and C become unfavorably large and impossible to correctby another surface because the surfaces B and C are assigned the greaterpart of the overall power of the optical system.

It is even more desirable to satisfy the following condition:

0.8<αbc<1.2  (7-1)

It is still more desirable to satisfy the following condition:

0.9<αbc<1.1  (7-2)

Next, in a case where the prism object-side part has at least tworeflecting surfaces, when the powers in the X- and Y-axis directions ofthe first reflecting surface are denoted by Px1 and Py1, respectively,and the powers in the X- and Y-axis directions of the prism are denotedby Px and Py, respectively, it is preferable to satisfy the followingcondition:

−5<Px1/Px<0  (8)

If Px1/Px is not larger than the lower limit of the condition (8), i.e.−5, the negative power of the first reflecting surface becomesexcessively strong. Consequently, decentration aberrations, particularlyimage distortion due to decentration, produced by this surface becomelarge and hence difficult to correct by another surface. If Px1/Px isnot smaller than the upper limit of the condition (8), i.e. 0, aretrofocus type optical system cannot be realized, and it becomesdifficult to ensure a wide field angle for observation.

To ensure a horizontal half field angle of 15° or more, in particular,it is even more desirable to satisfy the following condition:

−3<Px1/Px<−0.3  (8-1)

It is also preferable to satisfy the following condition:

−4<Py1/Py<0  (9)

If Py1/Py is not larger than the lower limit of the condition (9), i.e.−4, the negative power of the first reflecting surface becomesexcessively strong. Consequently, decentration aberrations, particularlyimage distortion due to decentration, produced by this surface becomelarge and hence difficult to correct by another surface. If Py1/Py isnot smaller than the upper limit of the condition (9), i.e. 0, aretrofocus type optical system cannot be realized, and it becomesdifficult to ensure a wide field angle for observation.

To ensure a horizontal half field angle of 15° or more, in particular,it is even more desirable to satisfy the following condition:

−2<Py1/Py<−0.1  (9-1)

When the powers in the X- and Y-axis directions of the second reflectingsurface are denoted by Px2 and Py2, respectively, and the powers in theX- and Y-axis directions of the prism are denoted by Px and Py,respectively, it is preferable to satisfy the following condition:

−2<Px2/Px<4  (10)

The condition (10) is a condition for the second reflecting surface. Thesecond reflecting surface reflects rays at a large angle to lead them tothe image plane. Accordingly, the angle at which rays are incident onthe second reflecting surface is large. If Px2/Px is not larger than thelower limit of the condition (10), i.e. −2, or not smaller than theupper limit, i.e. 4, the second reflecting surface has an excessivelystrong power. Consequently, decentration aberrations produced by thissurface become excessively large and hence impossible to correct byanother surface. Because the second reflecting surface is relativelyclose to the stop position, decentration aberrations, particularly comadue to decentration, produced by this surface become large and hencedifficult to correct by another surface.

It is even more desirable to satisfy the following condition:

−1<Px2/Px<2  (10-1)

It is still more desirable to satisfy the following condition:

−0.4<Px2/Px<1  (10-2)

It is also preferable to satisfy the following condition:

−2<Py2/Py<2  (11)

The condition (11) is also a condition for the second reflectingsurface. The second reflecting surface reflects rays at a large angle tolead them to the image plane. Accordingly, the angle at which rays areincident on the second reflecting surface is large. If Py2/Py is notlarger than the lower limit of the condition (11), i.e. −2, or notsmaller than the upper limit, i.e. 2, the second reflecting surface hasan excessively strong power. Consequently, decentration aberrationsproduced by this surface become excessively large and hence impossibleto correct by another surface. Because the second reflecting surface isrelatively close to the stop position, decentration aberrations,particularly coma due to decentration, produced by this surface becomelarge and hence difficult to correct by another surface.

It is even more desirable to satisfy the following condition:

−1<Py2/Py<0.8  (11-1)

It is still more desirable to satisfy the following condition:

−0.8<Py2/Py<0.4  (11-2)

In the image-forming optical system according to the present invention,focusing of the image-forming optical system can be effected by movingall the constituent elements or moving the prism. However, it is alsopossible to effect focusing by moving the image-formation plane in thedirection of the axial principal ray exiting from the surface closest tothe image side. By doing so, it is possible to prevent displacement ofthe axial principal ray on the entrance side due to focusing even if thedirection in which the axial principal ray from the object enters theoptical system is not coincident with the direction of the axialprincipal ray exiting from the surface closest to the image side owingto the decentration of the image-forming optical system. It is alsopossible to effect focusing by moving a plurality of wedge-shapedprisms, which are formed by dividing a plane-parallel plate, in adirection perpendicular to the Z-axis. In this case also, focusing canbe performed independently of the decentration of the image-formingoptical system.

In the present invention, temperature compensation can be made byforming the prism object-side part and the prism image-side part usingdifferent materials. By providing the prism object-side part and theprism image-side part with powers of different signs, it is possible toprevent the focal shift due to changes in temperature, which is aproblem arising when a plastic material is used to form a prism.

In a case where the two prism parts of the present invention arecemented together, it is desirable that each of the two prism partsshould have a positioning portion for setting a relative position on asurface having no optical action. In a case where two prism parts eachhaving a reflecting surface with a power are cemented together as in thepresent invention, in particular, relative displacement of each prismpart causes the performance to be deteriorated. Therefore, in thepresent invention, a positioning portion for setting a relative positionis provided on each surface of each prism part that has no opticalaction, thereby ensuring the required positional accuracy. Thus, thedesired performance can be ensured. In particular, if the two prismparts are integrated into one unit by using the positioning portions andcoupling members, it becomes unnecessary to perform assembly adjustment.Accordingly, the cost can be further reduced.

Furthermore, the optical path can be folded in a direction differentfrom the decentration direction of the image-forming optical systemaccording to the present invention by placing a reflecting opticalmember, e.g. a mirror, on the object side of the entrance surface of theimage-forming optical system. By doing so, the degree of freedom forlayout of the image-forming optical system further increases, and theoverall size of the image-forming optical apparatus can be furtherreduced.

In the present invention, the image-forming optical system can be formedfrom a prism alone. By doing so, the number of components is reduced,and the cost is lowered. Furthermore, two prisms may be integrated intoone prism with a stop put therebetween. By doing so, the cost can befurther reduced.

In the present invention, the image-forming optical system may includeanother lens (positive or negative lens) as a constituent element inaddition to the prism at either or each of the object and image sides ofthe prism.

The image-forming optical system according to the present invention maybe a fast, single focal length lens system. Alternatively, theimage-forming optical system may be arranged in the form of a zoom lenssystem (variable-magnification image-forming optical system) bycombining it with a single or plurality of refracting optical systemsthat may be provided on the object or image side of the prism.

In the present invention, the refracting and reflecting surfaces of theimage-forming optical system may be formed from spherical surfaces orrotationally symmetric aspherical surfaces.

In a case where the above-described image-forming optical systemaccording to the present invention is placed in an image pickup part ofan image pickup apparatus, or in a case where the image pickup apparatusis a photographic apparatus having a camera mechanism, it is possible toadopt an arrangement in which a prism member is placed closest to theobject side among optical elements having an optical action, and theentrance surface of the prism member is decentered with respect to theoptical axis, and further a cover member is placed on the object side ofthe prism member at right angles to the optical axis. The arrangementmay also be such that the prism member has on the object side thereof anentrance surface decentered with respect to the optical axis, and acover lens having a power is placed on the object side of the entrancesurface of the prism member in coaxial relation to the optical axis soas to face the entrance surface across an air spacing.

If a prism member is placed closest to the object side and a decenteredentrance surface is provided on the front side of a photographicapparatus as stated above, the obliquely tilted entrance surface is seenfrom the subject, and it gives the illusion that the photographic centerof the apparatus is deviated from the subject when the entrance surfaceis seen from the subject side. Therefore, a cover member or a cover lensis placed at right angles to the optical axis, thereby preventing thesubject from feeling incongruous when seeing the entrance surface, andallowing the subject to be photographed with the same feeling as in thecase of general photographic apparatus.

A finder optical system can be formed by using any of theabove-described image-forming optical systems according to the presentinvention as a finder objective optical system and adding animage-inverting optical system for erecting an object image formed bythe finder objective optical system and an ocular optical system.

In addition, it is possible to construct a camera apparatus by using thefinder optical system and an objective optical system for photographyprovided in parallel to the finder optical system.

In addition, an image pickup optical system can be constructed by usingany of the foregoing image-forming optical systems according to thepresent invention and an image pickup device placed in an image planeformed by the image-forming optical system.

In addition, a camera apparatus can be constructed by using any of theforegoing image-forming optical systems according to the presentinvention as an objective optical system for photography, and a finderoptical system placed in an optical path separate from an optical pathof the objective optical system for photography or in an optical pathsplit from the optical path of the objective optical system forphotography.

In addition, an electronic camera apparatus can be constructed by usingany of the foregoing image-forming optical systems according to thepresent invention, an image pickup device placed in an image planeformed by the image-forming optical system, a recording medium forrecording image information received by the image pickup device, and animage display device that receives image information from the recordingmedium or the image pickup device to form an image for observation.

In addition, an endoscope system can be constructed by using anobservation system having any of the foregoing image-forming opticalsystems according to the present invention and an image transmittingmember for transmitting an image formed by the image-forming opticalsystem along a longitudinal axis, and an illumination system having anilluminating light source and an illuminating light transmitting memberfor transmitting illuminating light from the illuminating light sourcealong the longitudinal axis.

Still other objects and advantages of the invention will in part beobvious and will in part be apparent from the specification.

The invention accordingly comprises the features of construction,combinations of elements, and arrangement of parts which will beexemplified in the construction hereinafter set forth, and the scope ofthe invention will be indicated in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of an image-forming optical system accordingto Example 1 of the present invention.

FIG. 2 is a sectional view of an image-forming optical system accordingto Example 2 of the present invention.

FIG. 3 is a sectional view of an image-forming optical system accordingto Example 3 of the present invention.

FIG. 4 is a sectional view of an image-forming optical system accordingto Example 4 of the present invention.

FIG. 5 is a sectional view of an image-forming optical system accordingto Example 5 of the present invention.

FIG. 6 is a sectional view of an image-forming optical system accordingto Example 6 of the present invention.

FIG. 7 is a sectional view of an image-forming optical system accordingto Example 10 of the present invention.

FIG. 8 is a sectional view of an image-forming optical system accordingto Example 13 of the present invention.

FIG. 9 is a sectional view of an image-forming optical system accordingto Example 15 of the present invention.

FIG. 10 is an aberrational diagram showing lateral aberrations in theimage-forming optical system according to Example 1.

FIG. 11 is a perspective view showing the external appearance of anelectronic camera to which an image-forming optical system according tothe present invention is applied, as viewed from the front side thereof.

FIG. 12 is a perspective view of the electronic camera shown in FIG. 11,as viewed from the rear side thereof.

FIG. 13 is a sectional view showing the arrangement of the electroniccamera in FIG. 11.

FIG. 14 is a conceptual view of another electronic camera to which animage-forming optical system according to the present invention isapplied.

FIG. 15 is a conceptual view of a video endoscope system to which animage-forming optical system according to the present invention isapplied.

FIG. 16 is a conceptual view showing an arrangement in which a prismoptical system according to the present invention is applied to aprojection optical system of a presentation system.

FIG. 17 is a diagram showing a desirable arrangement for animage-forming optical system according to the present invention when itis placed in front of an image pickup device.

FIG. 18 is a conceptual view for describing curvature of field producedby a decentered reflecting surface.

FIG. 19 is a conceptual view for describing astigmatism produced by adecentered reflecting surface.

FIG. 20 is a conceptual view for describing coma produced by adecentered reflecting surface.

FIG. 21 is a diagram for describing the definition of the power of adecentered optical system and the power of a decentered optical surface.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Examples 1 to 15 of the image-forming optical system according to thepresent invention will be described below. It should be noted thatconstituent parameters of each example will be shown later.

In each example, as shown in FIG. 1, an axial principal ray 1 is definedby a ray emanating from the center of an object and passing through thecenter of a stop 2 to reach the center of an image plane 3. A hypotheticplane is taken in a plane extending through the intersection between theaxial principal ray 1 and an entrance surface (first surface) 11 of aprism 10 at right angles to the axial principal ray 1 entering theentrance surface 11. Another hypothetic plane is taken in a planeextending through the intersection between the axial principal ray 1 andan exit surface (surface A) A of the prism 10 at right angles to theaxial principal ray 1 exiting from the exit surface A. Further, areference plane is taken in a stop (pupil) plane 2. The intersection ofeach hypothetic plane and the associated optical surface and theintersection between the axial principal ray 1 and the stop plane 2 areeach defined as the origin for decentered optical surfaces presentbetween the optical surface and the stop plane 2 or the hypothetic planesubsequent thereto (the image plane in the case of the final hypotheticplane). In the case of the hypothetic plane determined with respect tothe intersection of the entrance surface and in the case of the stopplane 2, a Z-axis is taken in the direction of the axial principal ray 1incident thereon. In the case of the hypothetic plane determined withrespect to the intersection of the exit surface, a Z-axis is taken inthe direction of the axial principal ray 1 exiting from the exitsurface. With respect to the first hypothetic plane passing through theintersection between the axial principal ray 1 and the entrance surface(first surface) 11 of the prism 10, a positive direction of the Z-axisis taken in the direction of travel of the axial principal ray 1. Withrespect to the stop plane 2 and the hypothetic plane regarding the exitsurface, a positive direction of the Z-axis is taken in the direction oftravel of the axial principal ray 1 in a case where there are an evennumber of reflections in the optical path from the first hypotheticplane to the stop plane 2 or from the stop plane 2 to the subsequenthypothetic plane. In a case where the number of reflections is an oddnumber, a positive direction of the Z-axis is taken in an oppositedirection to the direction of travel of the axial principal ray 1. Aplane containing the Z-axis and the center of the image plane 3 isdefined as a YZ-plane. An axis extending through the origin at rightangles to the YZ-plane is defined as an X-axis. The direction in whichthe X-axis extends from the obverse side toward the reverse side of theplane of the figure is defined as a positive direction of the X-axis. Anaxis that constitutes a right-handed orthogonal coordinate system incombination with the X- and Z-axes is defined as a Y-axis. FIG. 1 showsthe hypothetic planes and a coordinate system concerning the firsthypothetic plane determined with respect to the intersection of theentrance surface 11. Illustration of the hypothetic planes and thecoordinate system is omitted in FIG. 2 and the subsequent figures.

In Example 1 to 15, the decentration of each surface is made in theYZ-plane, and the one and only plane of symmetry of each rotationallyasymmetric free-form surface is the YZ-plane.

Regarding decentered surfaces, each surface is given displacements inthe X-, Y- and Z-axis directions (X, Y and Z, respectively) of thevertex position of the surface from the origin of the associatedcoordinate system, and tilt angles (degrees) of the center axis of thesurface [the Z-axis of the above equation (a) in regard to free-formsurfaces] with respect to the X-, Y- and Z-axes (α, β and γ,respectively). In this case, positive α and β mean counterclockwiserotation relative to the positive directions of the corresponding axes,and positive γ means clockwise rotation relative to the positivedirection of the Z-axis.

Among optical surfaces constituting the optical system in each example,a specific surface (including a hypothetic plane) and a surfacesubsequent thereto are given a surface separation when these surfacesform a coaxial optical system. In addition, the refractive index andAbbe's number of each medium are given according to the conventionalmethod. It should be noted that the sign of the surface separation isshown to be a positive value in a case where there are an even number ofreflections in the optical path from the first hypothetic plane to thereference optical surface (including a hypothetic plane), whereas in acase where the number of reflections is an odd number, the sign of thesurface separation is shown to be a negative value. However, thedistances in the direction of travel of the axial principal ray 1 areall positive values.

The configuration of each free-form surface used in the presentinvention is defined by the above equation (a). The Z-axis of thedefining equation is the axis of the free-form surface.

In the constituent parameters (shown later), those terms concerningfree-form surfaces for which no data is shown are zero. The refractiveindex is expressed by the refractive index for the spectral d-line(wavelength: 587.56 nanometers). Lengths are given in millimeters.

Free-form surfaces may also be defined by Zernike polynomials. That is,the configuration of a free-form surface may be defined by the followingequation (b). The Z-axis of the defining equation (b) is the axis ofZernike polynomial. A rotationally asymmetric surface is defined bypolar coordinates of the height of the Z-axis with respect to theXY-plane. In the equation (b), A is the distance from the Z-axis in theXY-plane, and R is the azimuth angle about the Z-axis, which isexpressed by the angle of rotation measured from the Z-axis.

$\begin{matrix}{{x = {R \times {\cos (A)}}}{y = {{R \times {\sin (A)}Z} = {D_{2} + {D_{3}R\; {\cos (A)}} + {D_{4}R\; {\sin (A)}} + {D_{5}R^{2}{\cos \left( {2A} \right)}} + {D_{6}\left( {R^{2} - 1} \right)} + {D_{7}R^{2}{\sin \left( {2A} \right)}} + {D_{8}R^{3}{\cos \left( {3A} \right)}} + {{D_{9}\left( {{3R^{3}} - {2R}} \right)}{\cos (A)}} + {{D_{10}\left( {{3R^{3}} - {2R}} \right)}{\sin (A)}} + {D_{11}R^{3}{\sin \left( {3A} \right)}} + {D_{12}R^{4}{\cos \left( {4A} \right)}} + {{D_{13}\left( {{4R^{4}} - {3R^{2}}} \right)}{\cos \left( {2A} \right)}} + {D_{14}\left( {{6R^{4}} - {6R^{2}} + 1} \right)} + {{D_{15}\left( {{4R^{4}} - {3R^{2}}} \right)}{\sin \left( {2A} \right)}} + {D_{16}R^{4}{\sin \left( {4A} \right)}} + {D_{17}R^{5}{\cos \left( {5A} \right)}} + {{D_{18}\left( {{5R^{5}} - {4R^{3}}} \right)}{\cos \left( {3A} \right)}} + {{D_{19}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}{\cos (A)}} + {{D_{20}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}{\sin (A)}} + {{D_{21}\left( {{5R^{5}} - {4R^{3}}} \right)}{\sin \left( {3A} \right)}} + {D_{22}R^{5}{\sin \left( {5A} \right)}} + {D_{23}R^{6}{\cos \left( {6A} \right)}} + {{D_{24}\left( {{6R^{6}} - {5R^{4}}} \right)}{\cos \left( {4A} \right)}} + {{D_{25}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}{\cos \left( {2A} \right)}} + {D_{26}\left( {{20R^{6}} - {30R^{4}} + {12R^{2}} - 1} \right)} + {{D_{27}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}{\sin \left( {2A} \right)}} + {{D_{28}\left( {{6R^{6}} - {5R^{4}}} \right)}{\sin \left( {4A} \right)}} + {D_{29}R^{6}{\sin \left( {6A} \right)}}}}}} & (b)\end{matrix}$

In the above equation, to design an optical system symmetric withrespect to the X-axis direction, D₄, D₅, D₆, D₁₀, D₁₁, D₁₂, D₁₃, D₁₄,D₂₀, D₂₁, D₂₂ . . . should be used.

Other examples of surfaces usable in the present invention are expressedby the following defining equation (c):

Z=ΣΣC_(nm)XY

Assuming that k=7 (polynomial of degree 7), for example, a free-formsurface is expressed by an expanded form of the above equation asfollows:

$\begin{matrix}{Z = {C_{2} + {C_{3}y} + {C_{4}{x}} + {C_{5}y^{2}} + {C_{6}y{x}} + {C_{7}x^{2}} + {C_{8}y^{3}} + {C_{9}y^{2}{x}} + {C_{10}{yx}^{2}} + {C_{11}{x^{3}}} + {C_{12}y^{4}} + {C_{13}y^{3}{x}} + {C_{14}y^{2}x^{2}} + {C_{15}y{x^{3}}} + {C_{16}x^{4}} + {C_{17}y^{5}} + {C_{18}y^{4}{x}} + {C_{19}y^{3}x^{2}} + {C_{20}y^{2}{x^{3}}} + {C_{21}{yx}^{4}} + {C_{22}{x^{5}}} + {C_{23}y^{6}} + {C_{24}y^{5}{x}} + {C_{25}y^{4}x^{2}} + {C_{26}y^{3}{x^{3}}} + {C_{27}y^{2}x^{4}} + {C_{28}y{x^{5}}} + {C_{29}x^{6}} + {C_{30}y^{7}} + {C_{31}y^{6}{x}} + {C_{32}y^{5}x^{2}} + {C_{33}y^{4}{x^{3}}} + {C_{34}y^{3}x^{4}} + {C_{35}y^{2}{x^{5}}} + {C_{36}{yx}^{6}} + {C_{37}{x^{7}}}}} & (c)\end{matrix}$

Although in the examples of the present invention the surfaceconfiguration is expressed by a free-form surface using the aboveequation (a), it should be noted that the same advantageous effect canbe obtained by using the above equation (b) or (c).

In all Examples 1 to 15, photographic field angles are as follows: Thehorizontal half field angle is 26.3°, and the vertical half field angleis 20.3°. The size of the image pickup device is 3.2×2.4 millimeters.F-number is 2.8. The focal length is equivalent to about 3.27millimeters. The image-forming optical system according to each examplecan be applied to other sizes, as a matter of course. The presentinvention includes not only an image pickup optical system using theimage-forming optical system according to the present invention but alsoan image pickup apparatus incorporating the optical system.

Examples 1 and 7

FIG. 1 is a sectional view of Example 1 taken along the YZ-planecontaining the axial principal ray. The sectional view of Example 7 issimilar to FIG. 1. Therefore, illustration of Example 7 is omitted.Constituent parameters of these examples will be shown later. In theconstituent parameters, free-form surfaces are denoted by “FFS”, andhypothetic planes by “HRP” (Hypothetic Reference Plane). The same shallapply to the other examples.

Examples 1 and 7 each have, in order in which light passes from theobject side, an object-side part of a prism 10, a stop 2, an image-sidepart of the prism 10, and an image plane (image-formation plane) 3. Theobject-side part of the prism 10 comprises an entrance surface 11 as afirst surface, a first reflecting surface 12, and a second reflectingsurface 13 formed from the first surface 11, which also serves as theentrance surface 11. The image-side part of the prism 10 comprises asurface C as a third reflecting surface, a surface B as a fourthreflecting surface, and a surface A as an exit surface. Rays from anobject enter through the entrance surface 11 and are reflectedsuccessively by the first reflecting surface 12 and the secondreflecting surface 13. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.In the object-side part of the prism 10, the entrance surface 11 and thesecond reflecting surface 13 are the identical optical surface havingboth transmitting and reflecting actions.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 2 to 5 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 1. The displacements of eachof the surface Nos. 6 to 9 are expressed by the amounts of displacementfrom the stop plane 2 of surface No. 5. The image plane is expressed byonly the surface separation along the axial principal ray from thehypothetic plane 2 of surface No. 9.

Examples 2 and 8

FIG. 2 is a sectional view of Example 2 taken along the YZ-planecontaining the axial principal ray. The sectional view of Example 8 issimilar to FIG. 2. Therefore, illustration of Example 8 is omitted.Constituent parameters of these examples will be shown later.

Examples 2 and 8 each have, in order in which light passes from theobject side, an object-side part of a prism 10, a stop 2, an image-sidepart of the prism 10, and an image plane (image-formation plane) 3. Theobject-side part of the prism 10 comprises an entrance surface 11 as afirst surface, a first reflecting surface 12, and a second reflectingsurface 13 formed from the first surface 11, which also serves as theentrance surface 11. The image-side part of the prism 10 comprises asurface C as a third reflecting surface, a surface B as a fourthreflecting surface, and a surface A as an exit surface. Rays from anobject enter through the entrance surface 11 and are reflectedsuccessively by the first reflecting surface 12 and the secondreflecting surface 13. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.In the object-side part of the prism 10, the entrance surface 11 and thesecond reflecting surface 13 are the identical optical surface havingboth transmitting and reflecting actions. It should be noted thatExamples 2 and 8 differ from Examples 1 and 7 in that the direction inwhich the rays are reflected from the surface C in Examples 2 and 8 isopposite to that in Examples 1 and 7.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 2 to 5 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 1. The displacements of eachof the surface Nos. 6 to 9 are expressed by the amounts of displacementfrom the stop plane 2 of surface No. 5. The image plane is expressed byonly the surface separation along the axial principal ray from thehypothetic plane 2 of surface No. 9.

Examples 3 and 9

FIG. 3 is a sectional view of Example 3 taken along the YZ-planecontaining the axial principal ray. The sectional view of Example 9 issimilar to FIG. 3. Therefore, illustration of Example 9 is omitted.Constituent parameters of these examples will be shown later.

Examples 3 and 9 each have, in order in which light passes from theobject side, an object-side part of a prism 10, a stop 2, an image-sidepart of the prism 10, and an image plane (image-formation plane) 3. Theobject-side part of the prism 10 comprises an entrance surface 11 as afirst surface, a first reflecting surface 12, and a second reflectingsurface 13. The image-side part of the prism 10 comprises a surface C asa third reflecting surface, a surface B as a fourth reflecting surface,and a surface A as an exit surface. Rays from an object enter throughthe entrance surface 11 and are reflected successively by the firstreflecting surface 12 and the second reflecting surface 13. Then, therays pass through the stop (pupil) 2 and are reflected successively bythe surface C and the surface B and then pass through the surface A toform an image on the image plane 3.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 2 to 5 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 1. The displacements of eachof the surface Nos. 6 to 9 are expressed by the amounts of displacementfrom the stop plane 2 of surface No. 5. The image plane is expressed byonly the surface separation along the axial principal ray from thehypothetic plane 2 of surface No. 9.

Examples 4, 10 and 13

FIGS. 4, 7 and 8 are sectional views of Examples 4, 10 and 13,respectively, taken along the YZ-plane containing the axial principalray. Constituent parameters of these examples will be shown later.

Examples 4, 10 and 13 each have, in order in which light passes from theobject side, an object-side part of a prism 10, a stop 2, an image-sidepart of the prism 10, and an image plane (image-formation plane) 3. Theobject-side part of the prism 10 comprises an entrance surface 11 as afirst surface, a first reflecting surface 12, and a second reflectingsurface 13. The image-side part of the prism 10 comprises a surface C asa third reflecting surface, a surface B as a fourth reflecting surface,and a surface A as an exit surface. Rays from an object enter throughthe entrance surface 11 and are reflected successively by the firstreflecting surface 12 and the second reflecting surface 13. Then, therays pass through the stop (pupil) 2 and are reflected successively bythe surface C and the surface B and then pass through the surface A toform an image on the image plane 3. It should be noted that Examples 4,10 and 13 differ from Examples 3 and 9 in that the direction in whichthe rays are reflected from the surface C in Examples 4, 10 and 13 isopposite to that in Examples 3 and 9.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 2 to 5 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 1. The displacements of eachof the surface Nos. 6 to 9 are expressed by the amounts of displacementfrom the stop plane 2 of surface No. 5. The image plane is expressed byonly the surface separation along the axial principal ray from thehypothetic plane 2 of surface No. 9.

Examples 5, 11 and 14

FIG. 5 is a sectional view of Example 5 taken along the YZ-planecontaining the axial principal ray. The sectional views of Examples 11and 14 are similar to FIG. 5. Therefore, illustration of Examples 11 and14 is omitted. Constituent parameters of these examples will be shownlater.

Examples 5, 11 and 14 each have, in order in which light passes from theobject side, an object-side part of a prism 10, a stop 2, an image-sidepart of the prism 10, and an image plane (image-formation plane) 3. Theobject-side part of the prism 10 comprises an entrance surface 11 as afirst surface, a first reflecting surface 12, a second reflectingsurface 13 formed from the first surface 11, which also serves as theentrance surface 11, and a third reflecting surface 14. The image-sidepart of the prism 10 comprises a surface C as a fourth reflectingsurface, a surface B as a fifth reflecting surface, and a surface A asan exit surface. Rays from an object enter through the entrance surface11 and are reflected successively by the first reflecting surface 12,the second reflecting surface 13 and the third reflecting surface 14.Then, the rays pass through the stop (pupil) 2 and are reflectedsuccessively by the surface C and the surface B and then pass throughthe surface A to form an image on the image plane 3. In the object-sidepart of the prism 10, the entrance surface 11 and the second reflectingsurface 13 are the identical optical surface having both transmittingand reflecting actions.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 2 to 6 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 1. The displacements of eachof the surface Nos. 7 to 10 are expressed by the amounts of displacementfrom the stop plane 2 of surface No. 6. The image plane is expressed byonly the surface separation along the axial principal ray from thehypothetic plane 2 of surface No. 10.

Examples 6, 12 and 15

FIGS. 6 and 9 are sectional views of Examples 6 and 15, respectively,taken along the YZ-plane containing the axial principal ray. Thesectional view of Example 12 is similar to these figures. Therefore,illustration of Example 12 is omitted. Constituent parameters of theseexamples will be shown later.

Examples 6, 12 and 15 each have, in order in which light passes from theobject side, an object-side part of a prism 10, a stop 2, an image-sidepart of the prism 10, and an image plane (image-formation plane) 3. Theobject-side part of the prism 10 comprises an entrance surface 11 as afirst surface, a first reflecting surface 12, a second reflectingsurface 13 formed from the first surface 11, which also serves as theentrance surface 11, and a third reflecting surface 14. The image-sidepart of the prism 10 comprises a surface C as a fourth reflectingsurface, a surface B as a fifth reflecting surface, and a surface A asan exit surface. Rays from an object enter through the entrance surface11 and are reflected successively by the first reflecting surface 12,the second reflecting surface 13 and the third reflecting surface 14.Then, the rays pass through the stop (pupil) 2 and are reflectedsuccessively by the surface C and the surface B and then pass throughthe surface A to form an image on the image plane 3. In the object-sidepart of the prism 10, the entrance surface 11 and the second reflectingsurface 13 are the identical optical surface having both transmittingand reflecting actions. It should be noted that Examples 6, 12 and 15differ from Examples 5, 11 and 14 in that the direction in which therays are reflected from the surface C in Examples 6, 12 and 15 isopposite to that in Examples 5, 11 and 14.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 2 to 6 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 1. The displacements of eachof the surface Nos. 7 to 10 are expressed by the amounts of displacementfrom the stop plane 2 of surface No. 6. The image plane is expressed byonly the surface separation along the axial principal ray from thehypothetic plane 2 of surface No. 10.

Constituent parameters in the foregoing Examples 1 to 15 are shownbelow. In the tables below, “FFS” denotes a free-form surface, and “HRP”denotes a hypothetic plane.

Example 1

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle around (3)} (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 9 ∞ (HRP2) 2.09 (7) Image ∞plane FFS{circle around (1)} C₄ 1.0213 × 10⁻³ C₆ 2.6453 × 10⁻³FFS{circle around (2)} C₄ 3.6831 × 10⁻² C₆ 3.1506 × 10⁻² FFS{circlearound (3)} C₄ −1.9619 × 10⁻²   C₆ −1.4927 × 10⁻²   FFS{circle around(4)} C₄ 1.4377 × 10⁻² C₆ 1.6300 × 10⁻² FFS{circle around (5)} C₄ 2.3346× 10⁻² C₆ 7.0472 × 10⁻² Displacement and tilt(1) X 0.00 Y 2.03 Z −0.55 α14.76 β 0.00 γ 0.00 Displacenment and tilt(2) X 0.00 Y 0.13 Z 1.46 α−19.14 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 3.85 Z 0.01 α72.95 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 0.00 Z 8.65 α−16.44 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 5.14 Z 0.70 α−15.34 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y 5.44 Z 8.55 α20.59 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y 5.44 Z 8.55 α−7.51 β 0.00 γ 0.00

Example 2

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle around (3)} (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 9 ∞ (HRP2) 1.90 (7) Image ∞plane FFS{circle around (1)} C₄ 2.0637 × 10⁻² C₆ −3.3192 × 10⁻³  FFS{circle around (2)} C₄ 3.0378 × 10⁻² C₆ 1.1176 × 10⁻² FFS{circlearound (3)} C₄ −5.5702 × 10⁻³   C₆ −1.7581 × 10⁻²   FFS{circle around(4)} C₄ 2.8728 × 10⁻² C₆ 1.8483 × 10⁻² FFS{circle around (5)} C₄ −1.3836× 10⁻⁴   C₆ 9.0601 × 10⁻² Displacement and tilt(1) X 0.00 Y 5.52 Z 0.61α −5.19 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y −0.17 Z 4.03 α−30.69 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 8.01 Z 2.80 α48.57 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 0.00 Z 6.01 α19.78 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y −4.37 Z 0.72 α18.78 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y −4.56 Z 6.08 α−15.78 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −4.56 Z 6.08 α5.04 β 0.00 γ 0.00

Example 3

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle around (4)} (5) 1.4924 57.6 7 FFS{circle around (5)} (6)1.4924 57.6 8 FFS{circle around (6)} (7) 9 ∞ (HRP2) 2.81 (8) Image ∞plane FFS{circle around (1)} C₄   4.7101 × 10⁻³ C₆ −1.2652 × 10⁻²  FFS{circle around (2)} C₄   1.5845 × 10⁻² C₆ 1.5053 × 10⁻² FFS{circlearound (3)} C₄ −1.3680 × 10⁻² C₆ 8.6156 × 10⁻³ FFS{circle around (4)} C₄−2.5267 × 10⁻² C₆ −5.4885 × 10⁻³   FFS{circle around (5)} C₄   1.9895 ×10⁻² C₆ 2.3998 × 10⁻² FFS{circle around (6)} C₄ −3.8200 × 10⁻³ C₆ 4.6234× 10⁻² Displacement and tilt(1) X 0.00 Y 0.00 Z 0.00 α 26.39 β 0.00 γ0.00 Displacement and tilt(2) X 0.00 Y 0.33 Z 2.08 α −25.10 β 0.00 γ0.00 Displacement and tilt(3) X 0.00 Y 4.84 Z −0.60 α −18.42 β 0.00 γ0.00 Displacement and tilt(4) X 0.00 Y 5.76 Z 1.63 α 22.43 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y 0.00 Z 3.70 α −25.27 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y 4.41 Z 0.07 α −27.00 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y 4.17 Z 4.08 α 18.86 β 0.00 γ 0.00Displacement and tilt(8) X 0.00 Y 4.17 Z 4.08 α −15.66 β 0.00 γ 0.00

Example 4

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle around (4)} (5) 1.4924 57.6 7 FFS{circle around (5)} (6)1.4924 57.6 8 FFS{circle around (6)} (7) 9 ∞ (HRP2) 2.62 (8) Image ∞plane FFS{circle around (1)} C₄ 2.8191 × 10⁻² C₆ 2.4229 × 10⁻²FFS{circle around (2)} C₄ 2.9443 × 10⁻² C₆ 1.5005 × 10⁻² FFS{circlearound (3)} C₄ 2.2659 × 10⁻² C₆ 5.5456 × 10⁻³ FFS{circle around (4)} C₄−1.7340 × 10⁻³   C₆ −7.3468 × 10⁻³   FFS{circle around (5)} C₄ 3.2881 ×10⁻² C₆ 2.3399 × 10⁻² FFS{circle around (6)} C₄ −2.2289 × 10⁻²   C₆6.9150 × 10⁻³ Displacement and tilt(1) X 0.00 Y 0.00 Z 0.00 α −19.38 β0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y −0.94 Z 8.19 α −33.31 β0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 7.82 Z 3.15 α −20.32 β0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 8.93 Z 6.31 α 19.46 β 0.00γ 0.00 Displacement and tilt(5) X 0.00 Y 0.00 Z 3.35 α 29.52 β 0.00 γ0.00 Displacement and tilt(6) X 0.00 Y −3.73 Z 1.11 α 26.00 β 0.00 γ0.00 Displacement and tilt(7) X 0.00 Y −4.02 Z 3.45 α −24.90 β 0.00 γ0.00 Displacement and tilt(8) X 0.00 Y −4.02 Z 3.45 α 2.36 β 0.00 γ 0.00

Example 5

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 FFS{circle around (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 1.4924 57.6 9 FFS{circle around(6)} (7) 10  ∞ (HRP2) −2.53 (8) Image ∞ plane FFS{circle around (1)} C₄3.2161 × 10⁻² C₆ 1.1132 × 10⁻² FFS{circle around (2)} C₄ 2.9358 × 10⁻²C₆ 2.4124 × 10⁻² FFS{circle around (3)} C₄ 4.5395 × 10⁻² C₆ 1.0726 ×10⁻² FFS{circle around (4)} C₄ 2.7116 × 10⁻² C₆ 2.2939 × 10⁻² FFS{circlearound (5)} C₄ −1.3722 × 10⁻²   C₆ −7.9613 × 10⁻³   FFS{circle around(6)} C₄ 1.0985 × 10⁻² C₆ −1.6177 × 10⁻³   Displacement and tilt(1) X0.00 Y 2.45 Z −0.60 α 12.05 β 0.00 γ 0.00 Displacement and tilt(2) X0.00 Y 0.20 Z 2.19 α −16.98 β 0.00 γ 0.00 Displacement and tilt(3) X0.00 Y 8.59 Z 2.51 α 11.60 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00Y 11.10 Z −0.47 α −39.95 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y0.00 Z −4.97 α 20.63 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y3.86 Z −0.57 α 16.79 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y4.45 Z −4.95 α −23.53 β 0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y4.45 Z −4.95 α 0.54 β 0.00 γ 0.00

Example 6

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 FFS{circle around (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 1.4924 57.6 9 FFS{circle around(6)} (7) 10  ∞ (HRP2) −2.48 (8) Image ∞ plane FFS{circle around (1)} C₄2.6501 × 10⁻² C₆ −4.4906 × 10⁻³ FFS{circle around (2)} C₄ 3.2328 × 10⁻²C₆   6.2858 × 10⁻³ FFS{circle around (3)} C₄ 4.6833 × 10⁻³ C₆ −9.1587 ×10⁻³ FFS{circle around (4)} C₄ 9.3385 × 10⁻³ C₆  1.0377 × 10⁻²FFS{circle around (5)} C₄ −3.0642 × 10⁻²   C₆ −1.8737 × 10⁻² FFS{circlearound (6)} C₄ −7.5684 × 10⁻³   C₆ −1.9285 × 10⁻² Displacement andtilt(1) X 0.00 Y 5.66 Z 1.47 α −13.02 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y −0.39 Z 4.18 α −35.62 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 9.18 Z 5.69 α 10.58 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 10.30 Z 2.39 α −18.65 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 0.00 Z −3.97 α −21.85 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y −3.21 Z −0.61 α −19.95 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y −3.44 Z −4.00 α 19.52 β 0.00 γ 0.00 Displacement andtilt(8) X 0.00 Y −3.44 Z −4.00 α −4.34 β 0.00 γ 0.00

Example 7

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle around (3)} (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 9 ∞ (HRP2) 2.09 (7) Image ∞plane FFS{circle around (1)} C₄ 1.8037 × 10⁻³ C₆ 5.9979 × 10⁻⁴ C₈−4.2189 × 10⁻³ C₁₀ −6.1622 × 10⁻⁴   FFS{circle around (2)} C₃ 2.9790 ×10⁻² C₆ 1.5970 × 10⁻² C₈ −6.6963 × 10⁻³ C₁₀ −2.2231 × 10⁻³   FFS{circlearound (3)} C₄ −2.4370 × 10⁻²   C₆ −1.1867 × 10⁻²   C₈ −2.7358 × 10⁻⁴C₁₀ 1.0226 × 10⁻⁴ FFS{circle around (4)} C₄ 3.9939 × 10⁻³ C₆ 1.8938 ×10⁻² C₇ −3.1418 × 10⁻⁵ C₁₀ 1.5226 × 10⁻⁴ FFS{circle around (5)} C₄−3.9043 × 10⁻²   C₆ 3.8003 × 10⁻² C₈  2.5494 × 10⁻² Displacement andtilt(1) X 0.00 Y 1.61 Z −0.85 α 27.52 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y 0.32 Z 1.90 α −7.70 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 8.75 Z 0.40 α 80.10 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 0.00 Z 6.64 α −18.90 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 4.62 Z 0.69 α −17.71 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y 4.85 Z 6.40 α 27.82 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y 4.85 Z 6.40 α −12.06 β 0.00 γ 0.00

Example 8

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle around (3)} (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 9 ∞ (HRP2) 1.12 (7) Image ∞plane FFS{circle around (1)} C₄   2.2304 × 10⁻² C₆ 6.7813 × 10⁻⁴ C₈1.1812 × 10⁻³ C₁₀ −3.3872 × 10⁻⁴ FFS{circle around (2)} C₄   3.1480 ×10⁻² C₆ 1.2842 × 10⁻² C₈ 2.0530 × 10⁻³ C₁₀ −2.3129 × 10⁻⁴ FFS{circlearound (3)} C₄ −8.7252 × 10⁻³ C₆ −1.4882 × 10⁻²   C₈ 1.2779 × 10⁻³ C₁₀−3.1090 × 10⁻⁴ FFS{circle around (4)} C₄   2.8592 × 10⁻² C₆ 2.1296 ×10⁻² C₈ −1.4838 × 10⁻⁵   C₁₀ −4.9595 × 10⁻⁴ FFS{circle around (5)} C₄  9.2639 × 10⁻² C₆ −1.7009 × 10⁻²   C₈ −1.9762 × 10⁻²   Displacement andtilt(1) X 0.00 Y 7.05 Z 0.64 α −6.42 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y −0.08 Z 4.76 α −30.48 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 8.88 Z 2.34 α 47.14 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 0.00 Z 5.52 α 20.19 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y −4.13 Z 0.67 α 18.77 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y −4.40 Z 6.02 α −7.46 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y −4.40 Z 6.02 α −0.55 β 0.00 γ 0.00

Example 9

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle around (4)} (5) 1.4924 57.6 7 FFS{circle around (5)} (6)1.4924 57.6 8 FFS{circle around (6)} (7) 9 ∞ (HRP2) 2.97 (8) Image ∞plane FFS{circle around (1)} C₄ −8.2788 × 10⁻³ C₆ 3.0759 × 10⁻² C₈  2.5136 × 10⁻³ FFS{circle around (2)} C₄   1.5271 × 10⁻² C₆ 6.5200 ×10⁻³ C₈   2.0313 × 10⁻⁴ C₁₀   3.8831 × 10⁻⁴ FFS{circle around (3)} C₄−7.1872 × 10⁻³ C₆ −2.8529 × 10⁻²   C₈ −1.0926 × 10⁻³ C₁₀ −1.1652 × 10⁻⁴FFS{circle around (4)} C₄ −2.5205 × 10⁻² C₆ −1.8722 × 10⁻²   C₈ −9.9093× 10⁻⁴ C₁₀ −3.7485 × 10⁻⁴ FFS{circle around (5)} C₄   1.2857 × 10⁻² C₆2.1262 × 10⁻² C₈ −7.0303 × 10⁻⁴ C₁₀ −4.4194 × 10⁻⁴ FFS{circle around(6)} C₄   1.0973 × 10⁻³ C₆ 3.2543 × 10⁻² C₈   1.1063 × 10⁻² Displacementand tilt(1) X 0.00 Y 0.00 Z 0.00 α 33.59 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y 1.10 Z 5.23 α −20.07 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 7.63 Z 0.12 α −16.48 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 8.56 Z 2.81 α 19.02 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 0.00 Z 4.81 α −24.08 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y 4.62 Z 0.67 α −21.89 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y 4.93 Z 4.68 α 28.01 β 0.00 γ 0.00 Displacement andtilt(8) X 0.00 Y 4.93 Z 4.68 α −8.73 β 0.00 γ 0.00

Example 10

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle around (4)} (5) 1.4924 57.6 7 FFS{circle around (5)} (6)1.4924 57.6 8 FFS{circle around (6)} (7) 9 ∞ (HRP2) 2.05 (8) Image ∞plane FFS{circle around (1)} C₄ 1.4974 × 10⁻² C₆ 3.0277 × 10⁻² C₈ 2.0441× 10⁻³ FFS{circle around (2)} C₄ 3.0398 × 10⁻² C₆ 1.2528 × 10⁻² C₈1.4776 × 10⁻³ C₁₀ 3.2717 × 10⁻⁴ FFS{circle around (3)} C₄ 2.7429 × 10⁻²C₆ 4.8497 × 10⁻³ C₈ 1.5116 × 10⁻³ C₁₀ 3.1159 × 10⁻⁴ FFS{circle around(4)} C₄ 1.4459 × 10⁻² C₆ −5.2512 × 10⁻³   C₈ 2.6999 × 10⁻³ C₁₀ 1.3731 ×10⁻³ FFS{circle around (5)} C₄ 4.5648 × 10⁻² C₆ 2.9908 × 10⁻² C₈ −1.8723× 10⁻⁴   C₁₀ 2.9008 × 10⁻⁵ FFS{circle around (6)} C₄ 9.6063 × 10⁻² C₆3.8186 × 10⁻² C₈ −1.4149 × 10⁻³   Displacement and tilt(1) X 0.00 Y 0.00Z 0.00 α 0.51 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.01 Z3.84 α −40.64 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 12.88 Z1.91 α −39.14 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 13.07 Z5.39 α 3.17 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 0.00 Z 3.67α 27.48 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y −3.89 Z 0.94 α26.31 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −4.03 Z 4.30 α−2.44 β 0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y −4.03 Z 4.30 α−2.29 β 0.00 γ 0.00

Example 11

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 FFS{circle around (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 1.4924 57.6 9 FFS{circle around(6)} (7) 10  ∞ (HRP2) −2.27 (8) Image ∞ plane FFS{circle around (1)} C₄3.5962 × 10⁻² C₆ 5.4714 × 10⁻³ C₈ 1.9678 × 10⁻⁴ C₁₀ −6.0817 × 10⁻⁵  FFS{circle around (2)} C₄ 1.9131 × 10⁻² C₆ 1.2344 × 10⁻² C₈ 1.5524 ×10⁻⁴ C₁₀ −4.1196 × 10⁻⁵   FFS{circle around (3)} C₄ 1.0316 × 10⁻¹ C₆7.4898 × 10⁻³ C₈ 1.3280 × 10⁻³ C₁₀ −2.1775 × 10⁻⁵   FFS{circle around(4)} C₄ 3.4735 × 10⁻² C₆ 1.2912 × 10⁻² C₈ 1.9341 × 10⁻³ C₁₀ 8.8579 ×10⁻⁴ FFS{circle around (5)} C₄ −1.9926 × 10⁻²   C₆ −2.9281 × 10⁻²   C₈1.0094 × 10⁻³ C₁₀ 3.2240 × 10⁻⁵ FFS{circle around (6)} C₄ 9.5170 × 10⁻³C₆ −1.0035 × 10⁻¹   C₈ −2.3170 × 10⁻³   C₁₀ 3.2652 × 10⁻³ Displacementand tilt(1) X 0.00 Y 3.96 Z −0.29 α 2.88 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y 0.09 Z 2.68 α −25.34 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 10.65 Z 3.85 α 5.78 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 13.10 Z 1.54 α −46.71 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 0.00 Z −4.20 α 24.79 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y 4.03 Z −0.77 α 22.24 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y 4.36 Z −4.45 α −10.22 β 0.00 γ 0.00 Displacement andtilt(8) X 0.00 Y 4.36 Z −4.45 α −2.56 β 0.00 γ 0.00

Example 12

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 FFS{circle around (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 1.4924 57.6 9 FFS{circle around(6)} (7) 10  ∞ (HRP2) −2.88 (8) Image ∞ plane FFS{circle around (1)} C₄2.0263 × 10⁻² C₆ 1.2117 × 10⁻² C₈ 1.0420 × 10⁻⁴ C₁₀ 2.5388 × 10⁻⁵FFS{circle around (2)} C₄ 3.0101 × 10⁻² C₆ 1.5268 × 10⁻² C₈ 1.0629 ×10⁻³ C₁₀ −3.5613 × 10⁻⁴   FFS{circle around (3)} C₄ −6.4453 × 10⁻³   C₆1.2679 × 10⁻² C₈ −9.5533 × 10⁻⁴   C₁₀ −2.3927 × 10⁻⁵   FFS{circle around(4)} C₄ −4.5819 × 10⁻³   C₆ −3.6206 × 10⁻⁴   C₈ −4.6337 × 10⁻³ C₁₀−1.8811 × 10⁻³   FFS{circle around (5)} C₄ −4.2725 × 10⁻²   C₆ −4.1080 ×10⁻²   C₈ −1.3108 × 10⁻³   C₁₀ 1.3700 × 10⁻⁴ FFS{circle around (6)} C₄−4.0288 × 10⁻²   C₆ −1.0079 × 10⁻¹   C₈ 7.3427 × 10⁻³ Displacement andtilt(1) X 0.00 Y 8.49 Z 2.91 α −24.96 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y −0.38 Z 4.92 α −40.79 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 10.84 Z 7.46 α −5.87 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 12.95 Z 4.86 α −39.03 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 0.00 Z −2.93 α −27.97 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y −3.17 Z −0.79 α −26.57 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y −3.28 Z −3.11 α 13.08 β 0.00 γ 0.00 Displacement andtilt(8) X 0.00 Y −3.28 Z −3.11 α −2.34 β 0.00 γ 0.00

Example 13

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle around (4)} (5) 1.4924 57.6 7 FFS{circle around (5)} (6)1.4924 57.6 8 FFS{circle around (6)} (7) 9 ∞ (HRP2) 2.19 (8) Image ∞plane FFS{circle around (1)} C₄   2.1612 × 10⁻² C₆   2.2441 × 10⁻² C₈  3.3142 × 10⁻³ C₁₃ −1.5450 × 10⁻⁶ FFS{circle around (2)} C₄   5.5239 ×10⁻² C₆   1.7639 × 10⁻² C₈   2.1076 × 10⁻³ C₁₀ −1.8254 × 10⁻⁶ C₁₁−3.3814 × 10⁻⁴ C₁₃ −7.3502 × 10⁻⁵ C₁₅ −6.3238 × 10⁻⁵ FFS{circle around(3)} C₄   3.2587 × 10⁻² C₆   9.7605 × 10⁻³ C₈   7.0727 × 10⁻⁴ C₁₀−6.4128 × 10⁻⁵ C₁₁ −3.0837 × 10⁻⁵ C₁₃ −9.0003 × 10⁻⁵ C₁₅ −6.1904 × 10⁻⁵FFS{circle around (4)} C₄   1.7641 × 10⁻² C₆ −3.1484 × 10⁻³ C₈   1.4327× 10⁻³ C₁₀   7.8898 × 10⁻⁴ C₁₁ −5.7451 × 10⁻⁴ C₁₃ −8.3755 × 10⁻⁴ C₁₅−2.4142 × 10⁻⁴ FFS{circle around (5)} C₄   5.2642 × 10⁻² C₆   3.6812 ×10⁻² C₈ −1.1918 × 10⁻³ C₁₀ −9.1978 × 10⁻⁴ C₁₁ −3.6615 × 10⁻⁴ C₁₃ −6.0092× 10⁻⁴ C₁₅ −1.8114 × 10⁻⁴ FFS{circle around (6)} C₄   1.1608 × 10⁻¹ C₆  1.5090 × 10⁻¹ C₈ −4.5791 × 10⁻³ C₁₃ −4.1698 × 10⁻³ Displacement andtilt(1) X 0.00 Y 0.00 Z 0.00 α −1.76 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y −0.04 Z 3.97 α −41.02 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 10.28 Z 2.41 α −40.73 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 10.28 Z 9.89 α 0.00 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 0.00 Z 3.35 α 29.33 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y −3.58 Z 1.17 α 28.72 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y −3.64 Z 3.78 α −3.74 β 0.00 γ 0.00 Displacement andtilt(8) X 0.00 Y −3.64 Z 3.78 α 0.00 β 0.00 γ 0.00

Example 14

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 FFS{circle around (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 1.4924 57.6 9 FFS{circle around(6)} (7) 10  ∞ (HRP2) −2.33 (8) Image ∞ plane FFS{circle around (1)} C₄  4.0827 × 10⁻² C₆   5.9635 × 10⁻³ C₈   1.1461 × 10⁻⁴ C₁₀ −2.1507 × 10⁻⁴C₁₁   5.1208 × 10⁻⁵ C₁₃ −3.2010 × 10⁻⁵ C₁₅ −6.7233 × 10⁻⁶ FFS{circlearound (2)} C₄   2.7721 × 10⁻² C₆   1.4635 × 10⁻² C₈   2.4781 × 10⁻⁴ C₁₀−2.2813 × 10⁻⁴ C₁₁ −2.5928 × 10⁻⁵ C₁₃ −7.5774 × 10⁻⁵ C₁₅ −2.0345 × 10⁻⁵FFS{circle around (3)} C₄   1.1023 × 10⁻¹ C₆   9.4811 × 10⁻³ C₈   3.2039× 10⁻³ C₁₀ −1.5865 × 10⁻⁴ C₁₁   2.8756 × 10⁻³ C₁₃   5.8910 × 10⁻⁴ C₁₅  3.1494 × 10⁻⁵ FFS{circle around (4)} C₄   3.4559 × 10⁻² C₆   1.5109 ×10⁻² C₈   1.9022 × 10⁻³ C₁₀   7.2864 × 10⁻⁴ C₁₁ −2.8143 × 10⁻⁵ C₁₃  2.4265 × 10⁻⁵ C₁₅ −3.0473 × 10⁻⁵ FFS{circle around (5)} C₄ −2.1578 ×10⁻² C₆ −2.9940 × 10⁻² C₈   8.7484 × 10⁻⁴ C₁₀ −1.7100 × 10⁻⁴ C₁₁  1.9611 × 10⁻⁶ C₁₃ −4.7297 × 10⁻⁵ C₁₅ −8.0783 × 10⁻⁵ FFS{circle around(6)} C₄   3.9290 × 10⁻³ C₆ −1.4942 × 10⁻¹ C₈ −9.2481 × 10⁻³ C₁₀ −4.6761× 10⁻³ C₁₁ −1.5588 × 10⁻³ C₁₃ −3.3748 × 10⁻³ C₁₅ −1.2423 × 10⁻²Displacement and tilt(1) X 0.00 Y 3.76 Z −0.37 α 4.15 β 0.00 γ 0.00Displacement and tilt(2) X 0.00 Y 0.12 Z 2.90 α −22.85 β 0.00 γ 0.00Displacement and tilt(3) X 0.00 Y 10.18 Z 3.90 α 5.11 β 0.00 γ 0.00Displacement and tilt(4) X 0.00 Y 12.22 Z 1.94 α −46.17 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y 0.00 Z −4.39 α 24.21 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y 4.03 Z −0.82 α 23.85 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y 4.08 Z −4.66 α −7.45 β 0.00 γ 0.00Displacement and tilt(8) X 0.00 Y 4.08 Z −4.66 α 2.64 β 0.00 γ 0.00

Example 15

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2 FFS{circlearound (1)} (1) 1.4924 57.6 3 FFS{circle around (2)} (2) 1.4924 57.6 4FFS{circle around (1)} (1) 1.4924 57.6 5 FFS{circle around (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle around (4)} (5)1.4924 57.6 8 FFS{circle around (5)} (6) 1.4924 57.6 9 FFS{circle around(6)} (7) 10  ∞ (HRP2) −3.07 (8) Image ∞ plane FFS{circle around (1)} C₄  2.3309 × 10⁻² C₆   9.9932 × 10⁻³ C₈   2.4136 × 10⁻⁴ C₁₀   1.1090 ×10⁻⁴ C₁₁   1.4334 × 10⁻⁴ C₁₃ −6.0188 × 10⁻⁵ C₁₅ −3.9163 × 10⁻⁶FFS{circle around (2)} C₄   4.1433 × 10⁻² C₆   1.6695 × 10⁻² C₈   1.5395× 10⁻³ C₁₀ −1.1536 × 10⁻⁴ C₁₁   2.0588 × 10⁻⁴ C₁₃ −1.5721 × 10⁻⁴ C₁₅−6.3666 × 10⁻⁵ FFS{circle around (3)} C₄ −9.6739 × 10⁻³ C₆   6.2716 ×10⁻³ C₈ −2.9572 × 10⁻⁵ C₁₀   4.3548 × 10⁻⁴ C₁₁   3.2750 × 10⁻⁴ C₁₃  1.5172 × 10⁻⁵ C₁₅   1.0324 × 10⁻⁴ FFS{circle around (4)} C₄   2.0722 ×10⁻³ C₆   6.4918 × 10⁻³ C₈ −4.2437 × 10⁻³ C₁₀ −1.9251 × 10⁻³ C₁₁  6.3713 × 10⁻⁴ C₁₃ −2.0539 × 10⁻⁶ C₁₅   3.2793 × 10⁻⁵ FFS{circle around(5)} C₄ −4.1173 × 10⁻² C₆ −3.7458 × 10⁻² C₈ −4.0580 × 10⁻³ C₁₀   2.3875× 10⁻⁴ C₁₁   3.7267 × 10⁻⁴ C₁₃   8.2371 × 10⁻⁴ C₁₅ −2.9197 × 10⁻⁵FFS{circle around (6)} C₄ −8.6169 × 10⁻² C₆ −1.5015 × 10⁻¹ C₈ −3.2168 ×10⁻² C₁₁ −4.0638 × 10⁻³ C₁₃ −6.9267 × 10⁻³ C₁₅ −8.1027 × 10⁻³Displacement and tilt(1) X 0.00 Y 8.37 Z 2.43 α −20.50 β 0.00 γ 0.00Displacement and tilt(2) X 0.00 Y −0.39 Z 5.35 α −37.89 β 0.00 γ 0.00Displacement and tilt(3) X 0.00 Y 11.32 Z 7.40 α 1.33 β 0.00 γ 0.00Displacement and tilt(4) X 0.00 Y 13.09 Z 4.04 α −27.92 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y 0.00 Z −2.14 α −35.59 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y −3.39 Z −0.99 α −35.28 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y −3.41 Z −2.53 α 9.75 β 0.00 γ 0.00Displacement and tilt(8) X 0.00 Y −3.41 Z −2.53 α −3.93 β 0.00 γ 0.00

FIG. 10 is an aberrational diagram showing lateral aberrations in theabove-described Example 1. In the diagram showing lateral aberrations,the numerals in the parentheses denote [horizontal (X-direction) fieldangle, vertical (Y-direction) field angle], and lateral aberrations atthe field angles are shown.

It should be noted that the values of the conditions (1) to (11) in theabove-described Examples 1 to 15 are as follows:

Cond. Ex. 1 Ex. 2 Ex. 3 Ex. 4 Ex. 5 Ex. 6 Ex. 7 Ex. 8 (1) 0.32 0.63 0.450.75 0.30 0.65 0.08 0.61 (2) 0.38 0.42 0.58 0.53 0.18 0.42 0.39 0.44 (3)0.44 0.12 0.57 0.04 0.60 0.20 0.51 0.19 (4) 0.35 0.40 0.13 0.17 0.510.23 0.24 0.31 (5) 16.84 21.59 22.97 33.64 23.33 24.47 19.42 22.35 (6)16.61 19.76 25.26 29.62 20.56 22.05 18.96 20.25 (7) 0.99 0.92 1.10 0.880.88 0.90 0.98 0.91 (8) −0.83 −0.66 −0.35 −0.67 −0.65 −0.69 −0.62 −0.68(9) −0.73 −0.25 −0.37 −0.34 −0.53 −0.14 −0.33 −0.26 (10)  0.02 0.45−0.31 0.51 0.71 0.56 0.04 0.48 (11)  0.06 −0.07 0.21 0.13 0.25 −0.100.01 0.01 Cond. Ex. 9 Ex. 10 Ex. 11 Ex. 12 Ex. 13 Ex. 14 Ex. 15 (1) 0.280.97 0.45 0.92 1.02 0.42 0.81 (2) 0.44 0.60 0.59 0.81 0.73 0.58 0.72 (3)0.54 −0.31 0.78 −0.10 −0.34 0.67 0.04 (4) 0.38 0.11 0.26 −0.01 0.06 0.290.12 (5) 25.62 29.35 26.54 30.06 30.83 23.65 36.89 (6) 24.38 27.56 24.8727.85 29.48 24.35 35.66 (7) 0.95 0.94 0.94 0.93 0.96 1.03 0.97 (8) −0.33−0.64 −0.43 −0.65 −1.08 −0.54 −0.81 (9) −0.13 −0.25 −0.25 −0.30 −0.35−0.29 −0.32 (10)  −0.16 0.58 0.81 0.43 0.63 0.80 0.46 (11)  −0.59 0.100.11 0.24 0.19 0.12 0.19

In the above-described examples, the object-side part of the prism 10,which constitute the image-forming optical system according to thepresent invention, uses a prism of the type in which there are two orthree internal reflections as stated in Examples 1 to 15. It should,however, be noted that prisms usable as the object-side part of theprism 10 in the image-forming optical system according to the presentinvention are not necessarily limited to the described type. Examples ofprisms usable in the present invention include a prism in which there isone internal reflection, and prisms arranged in the same way as inExamples 5, 6, 11, 12, 14 and 15 except that the first reflectingsurface 12 and the third reflecting surface 14 are formed from theidentical surface. It is also possible to use prisms arranged in thesame way as in Examples 5, 6, 11, 12, 14 and 15 except that the secondreflecting surface 13 is formed from a surface different from theentrance surface 11.

Incidentally, the above-described image-forming optical system accordingto the present invention can be used in photographic apparatus,particularly in cameras, in which an object image formed by theimage-forming optical system is received with an image pickup device,such as a CCD or a silver halide film, to take a photograph of theobject. It is also possible to use the image-forming optical system asan objective optical system of an observation apparatus in which anobject image is viewed through an ocular lens, particularly a finderunit of a camera. The image-forming optical system according to thepresent invention is also usable as an image pickup optical system foroptical apparatus using a small-sized image pickup device, e.g.endoscopes. Embodiments in which the present invention is applied tosuch apparatuses will be described below.

FIGS. 11 to 13 are conceptual views showing an arrangement in which theimage-forming optical system according to the present invention isincorporated into an objective optical system in a finder unit of anelectronic camera. FIG. 11 is a perspective view showing the externalappearance of an electronic camera 40 as viewed from the front sidethereof. FIG. 12 is a perspective view of the electronic camera 40 asviewed from the rear side thereof. FIG. 13 is a sectional view showingthe arrangement of the electronic camera 40. In the illustrated example,the electronic camera 40 includes a photographic optical system 41having an optical path 42 for photography, a finder optical system 43having an optical path 44 for the finder, a shutter 45, a flash 46, aliquid crystal display monitor 47, etc. When the shutter 45, which isplaced on the top of the camera 40, is depressed, photography isperformed through an objective optical system 48 for photography. Anobject image produced by the objective optical system 48 for photographyis formed on an image pickup surface 50 of a CCD 49 through a filter 51,e.g. a low-pass filter, an infrared cutoff filter, etc. The object imagereceived by the CCD 49 is processed in a processor 52 and displayed asan electronic image on the liquid crystal display monitor 47, which isprovided on the rear of the camera 40. The processor 52 is provided witha memory or the like to enable the photographed electronic image to berecorded. It should be noted that the memory may be provided separatelyfrom the processor 52. The arrangement may also be such that thephotographed electronic image is electronically recorded or written on afloppy disk or the like. The camera 40 may be arranged in the form of asilver halide camera in which a silver halide film is disposed in placeof the CCD 49.

Furthermore, an image-forming optical system similar to Example 4, byway of example, is placed in the optical path 44 for the finder as anobjective optical system 53 for the finder. In this case, a cover lens54 having a negative power is provided as a cover member to form a partof the objective optical system 53, thereby enlarging the field angle.It should be noted that the cover lens 54 and a part of the prism 10that is closer to the object side than the stop 2 constitute a frontunit of the objective optical system 53 for the finder, and a part ofthe prism 10 that is closer to the image side than the stop 2constitutes a rear unit of the objective optical system 53 for thefinder. An object image produced by the objective optical system 53 forthe finder is formed on a view frame 57 of a Porro prism 55, which is animage-erecting member. It should be noted that the view frame 57 isplaced between a first reflecting surface 56 and second reflectingsurface 58 of the Porro prism 55. An ocular optical system 59 is placedbehind the Porro prism 55 to lead an erect image to an observer'seyeball E.

In the camera 40, which is arranged as stated above, the objectiveoptical system 53 for the finder can be constructed with a minimalnumber of optical members. Accordingly, a high-performance and low-costcamera can be realized. In addition, because the optical path of theobjective optical system 53 can be folded, the degree of freedom withwhich the constituent elements can be arranged in the camera increases.This is favorable for design.

Although no mention is made of the arrangement of the objective opticalsystem 48 for photography in the electronic camera 40 shown in FIG. 13,it should be noted that the objective optical system 48 for photographymay be formed by using not only a refracting coaxial optical system butalso any of the image-forming optical systems, which comprises a singleprism 10, according to the present invention.

FIG. 14 is a conceptual view showing an arrangement in which animage-forming optical system according to the present invention isincorporated into an objective optical system 48 in a photography partof an electronic camera 40. In this example, an image-forming opticalsystem similar to Example 4 is used in the objective optical system 48for photography, which is placed in an optical path 42 for photography.An object image produced by the objective optical system 48 forphotography is formed on an image pickup surface 50 of a CCD 49 througha filter 51, e.g. a low-pass filter, an infrared cutoff filter, etc. Theobject image received by the CCD 49 is processed in a processor 52 anddisplayed in the form of an electronic image on a liquid crystal displaydevice (LCD) 60. The processor 52 also controls a recording device 61for recording the object image detected by the CCD 49 in the form ofelectronic information. The image displayed on the LCD 60 is led to anobserver's eyeball E through an ocular optical system 59. The ocularoptical system 59 is formed from a decentered prism having aconfiguration similar to that used in the image-forming optical systemaccording to the present invention. In this example, the ocular opticalsystem 59 has three surfaces, i.e. an entrance surface 62, a reflectingsurface 63, and a surface 64 serving as both reflecting and refractingsurfaces. At least one of the two reflecting surfaces 63 and 64,preferably each of them, is formed from a plane-symmetry free-formsurface with only one plane of symmetry that gives a power to a lightbeam and corrects decentration aberrations. The only one plane ofsymmetry is formed in approximately the same plane as the only one planeof symmetry of the plane-symmetry free-form surfaces in the prism 10provided in the objective optical system 48 for photography. Theobjective optical system 48 for photography may include another lens(positive or negative lens) as a constituent element on the object orimage side of the prism 10.

In the camera 40 arranged as stated above, the objective optical system48 for photography can be constructed with a minimal number of opticalmembers. Accordingly, a high-performance and low-cost camera can berealized. In addition, because all the constituent elements of theoptical system can be arranged in the same plane, it is possible toreduce the thickness in a direction perpendicular to the plane in whichthe constituent elements are arranged.

Although in this example a plane-parallel plate is placed as a covermember 65 of the objective optical system 48 for photography, it is alsopossible to use a lens having a power as the cover member 65 as in thecase of the above-described example.

The surface closest to the object side in the image-forming opticalsystem according to the present invention may be used as a cover memberinstead of providing a cover member separately. In this example, theentrance surface of the prism 10 is the closest to the object side inthe image-forming optical system. In such a case, however, because theentrance surface is decentered with respect to the optical axis, if thissurface is placed on the front side of the camera, it gives the illusionthat the photographic center of the camera 40 is deviated from thesubject when the entrance surface is seen from the subject side (thesubject normally feels that photographing is being performed in adirection perpendicular to the entrance surface, as in the case ofordinary cameras). Thus, the entrance surface would give a sense ofincongruity. Therefore, in a case where the surface of the image-formingoptical system that is closest to the object side is a decenteredsurface as in this example, it is desirable to provide the cover member65 (or cover lens 54) from the viewpoint of preventing the subject fromfeeling incongruous when seeing the entrance surface, and allowing thesubject to be photographed with the same feeling as in the case of theexisting cameras.

FIG. 15 is a conceptual view showing an arrangement in which animage-forming optical system according to the present invention isincorporated into an objective optical system 81 in an observationsystem of a video endoscope system. In this case, the objective opticalsystem 81 in the observation system uses an image-forming optical systemapproximately similar to Example 3. As shown in part (a) of FIG. 15, thevideo endoscope system includes a video endoscope 71, a light sourceunit 72 for supplying illuminating light, a video processor 73 forexecuting processing of signals associated with the video endoscope 71,a monitor 74 for displaying video signals output from the videoprocessor 73, a VTR deck 75 and a video disk 76, which are connected tothe video processor 73 to record video signals and so forth, and a videoprinter 77 for printing out video signals in the form of images. Thevideo endoscope system further includes a head-mounted image displayapparatus (HMD) 78. The video endoscope 71 has an insert part 79 with adistal end portion 80. The distal end portion 80 is arranged as shown inpart (b) of FIG. 15. A light beam from the light source unit 72 passesthrough a light guide fiber bundle 87 and illuminates a part to beobserved through an objective optical system 86 for illumination. Lightfrom the part to be observed enters an objective optical system 81 forobservation through a cover member 85. Thus, an object image is formedby the objective optical system 81. The object image is formed on animage pickup surface 84 of a CCD 83 through a filter 82, e.g. a low-passfilter, an infrared cutoff filter, etc. Furthermore, the object image isconverted into a video signal by the CCD 83. The video signal isdisplayed directly on the monitor 74 by the video processor 73, which isshown in part (a) of FIG. 15. In addition, the video signal is recordedin the VTR deck 75 and on the video disk 76 and also printed out in theform of an image from the video printer 77. In addition, the objectimage is displayed on the image display device of the HMD 78, therebyallowing a person wearing the HMD 78 to observe the displayed image.

The endoscope arranged as stated above can be constructed with a minimalnumber of optical members. Accordingly, a high-performance and low-costendoscope can be realized. Moreover, because the constituent portions ofthe single prism 10 of the objective optical system 81 in theobservation system are arranged in series in the direction of thelongitudinal axis of the endoscope, the above-described advantageouseffects can be obtained without hindering the achievement of a reductionin the diameter of the endoscope.

Incidentally, the image-forming optical system can also be used as aprojection optical system by reversing the optical path. FIG. 16 is aconceptual view showing an arrangement in which a prism optical systemaccording to the present invention is used in a projection opticalsystem 96 of a presentation system formed by combining together apersonal computer 90 and a liquid crystal projector 91. In this example,an image-forming optical system similar to Example 1 except that theoptical path is reverse to that in Example 1 is, used in the projectionoptical system 96. Referring to FIG. 16, image and manuscript dataprepared on the personal computer 90 is branched from a monitor outputand delivered to a processing control unit 98 in the liquid crystalprojector 91. In the processing control unit 98 of the liquid crystalprojector 91, the input data is processed and output to a liquid crystalpanel (LCP) 93. The liquid crystal panel 93 displays an imagecorresponding to the input image data. Light from a light source 92 isapplied to the liquid crystal panel 93. The amount of light transmittedby the liquid crystal panel 93 is determined by the gradation of theimage displayed on the liquid crystal panel 93. Light from the liquidcrystal panel 93 is projected on a screen 97 through a projectionoptical system 96 comprising a field lens 95 placed immediately in frontof the liquid crystal panel 93, a prism 10 constituting theimage-forming optical system according to the present invention, and acover lens 94 which is a positive lens.

The projector arranged as stated above can be constructed with a minimalnumber of optical members. Accordingly, a high-performance and low-costprojector can be realized. In addition, the projector can be constructedin a compact form.

FIG. 17 is a diagram showing a desirable arrangement for theimage-forming optical system according to the present invention when theimage-forming optical system is placed in front of an image pickupdevice, e.g. a CCD, or a filter. In the figure, a decentered prism P isa prism included in the image-forming optical system according to thepresent invention. When the image pickup surface D of an image pickupdevice forms a quadrangle as shown in the figure, it is desirable fromthe viewpoint of forming a beautiful image to place the decentered prismP so that the plane F of symmetry of a plane-symmetry free-form surfaceprovided in the decentered prism P is parallel to at least one of thesides forming the quadrangular image pickup surface D.

When the image pickup surface D has a shape in which each of the fourinterior angles is approximately 90 degrees, such as a square or arectangle, it is desirable that the plane F of symmetry of theplane-symmetry free-form surface should be parallel to two sides of theimage pickup surface D that are parallel to each other. It is moredesirable that the plane F of symmetry should lie at the middle betweentwo parallel sides and coincide with a position where the image pickupsurface D is in a symmetry between the right and left halves or betweenthe upper and lower halves. The described arrangement enables therequired assembly accuracy to be readily obtained when the image-formingoptical system is incorporated into an apparatus, and is useful formass-production.

When a plurality or all of the optical surfaces constituting thedecentered prism P, i.e. the entrance surface, the first reflectingsurface, the surface C, the surface B, the surface A, and so forth, areplane-symmetry free-form surfaces, it is desirable from the viewpoint ofdesign and aberration correcting performance to arrange the decenteredprism P so that the planes of symmetry of the plurality or all of theoptical surfaces are in the same plane F. In addition, it is desirablethat the plane F of symmetry and the image pickup surface D should be inthe above-described relationship.

As will be clear from the foregoing description, the present inventionmakes it possible to provide a high-performance and low-costimage-forming optical system with a minimal number of constituentoptical elements. In addition, it is possible to provide ahigh-performance image-forming optical system that is made compact andthin by folding an optical path using reflecting surfaces arranged tominimize the number of reflections.

1-29. (canceled)
 30. A catadioptric system comprising: at least one lens; and at least three reflecting surfaces; wherein when said three reflective surfaces are defined as a first reflecting surface, a second reflecting surface, and a third reflective surface in order along a light path, these reflecting surfaces are positioned so that a line connecting a point of reflection on the first reflecting surface, a point of reflection on the second reflecting surface and a point of reflection on the third reflecting surface does not intersect itself; at least one of the said first and second reflecting surfaces being a rotationally symmetric aspherical surface; said first reflecting surface and said third reflecting surface being connected to each other with a step interposed therebetween; said first reflecting surface and said third reflecting surface facing approximately in a same direction; and wherein a lens is positioned in an entrance-side light path entering a reflecting optical system formed from said three reflecting surfaces, and another lens is positioned in an exit-side light path exiting from said reflecting optical system. 